Yes, there is, but to see how and why we need a bit of exposition. Bear with me...
Definition
RU, in its more subtle versions designed to avoid "collapse" into AU,
construes right acts as acts permitted by a set of "ideal" rules the general
acceptance of which by most, but not all, people in the relevant community
would produce at least as much utility as comparable acceptance of other
moral codes. The rules are taken to be public, teachable, socially reinforced
rules that should be internalized by all. Such rules may include "built-in"
standard exceptions, but they would not be useful if they were too complex.
The rules in the "ideal" set or code may sometimes conflict, but allowing too
many conflicts among the rules would diminish their usefulness as rules. RU
can offer various procedures for resolving these conflicts, but to stipulate
that we should resolve conflicts simply by attempting to maximize utility in
each particular instance of conflict would threaten to undermine what is
distinctive about RU ... (Thomas E. Hill, Jr., 'Assessing Moral Rules: Utilitarian and Kantian Perspectives', Philosophical Issues, Vol. 15, Normativity (2005), pp. 158-178: 162.)
The crucial point
distinctive of RU [rule utilitarianism] is that it implies that particular acts in accord with a
useful rule can be right even though an alternative act [sanctioned by act utilitarianism] would actually
produce more utility - and particular acts contrary to useful rules can be
wrong even though they would actually produce more utility than
any alternative would. This feature, and the structure of RU, enables
rule-utilitarians to argue that the ideal moral code includes many intuitively
important moral rules regarding honesty, justice, gratitude, loyalty, etc,
that demand or forbid acts independently of the utility they produce on
the particular occasion. RU says it is right, not just a generally useful rule of
thumb, to conform to rules provided general acceptance of those rules by
most people in the relevant community produces at least as much utility as
such general acceptance of any alternative moral code.
Sophisticated versions of RU take into account that blindly following
rules ideal for a non-actual world might be disastrous (and morally wrong)
to follow in our imperfect, real world. Various strategies help to address the
problem: for example, in assessing the utility of general conformity to a
given set of rules we must take into account the feasibility and costs of
maintaining it as a moral code as well as legitimate expectations generated
under the actual moral code to be reformed ... (Hill: 163.)
First charge of arbitrariness
This is the charge that RU conflicts indefensibly with ordinary moral thinking. It:
entails judgments of right and wrong that conflict with judgments that are widely and
deeply held by most competent, reflective people. Just as AU (act utilitarianism) is said to
recommend acts that are unjust, ungrateful, breaches of promise, and
insensitive to moral deserts, it is charged that RU recommends moral
codes, or sets of rules, that are not adequately sensitive to claims of justice
gratitude, fidelity, and desert. The reason is that, although rules requiring
justice, fidelity, gratitude, and desert obviously promote well-being in many
ways, the moral code that maximizes (expected) utility (e.g., aggregate well
being) does not necessarily or obviously accord with our convictions about
these matters. Given the complexities of the relevant empirical facts, the
utility maximizing code would apparently allow many more exceptions than
our reflective moral convictions would.
The problem with this line of objection for present purposes is that we
are not in a position to know exactly what a utility maximizing code would
prescribe regarding matters involving justice, fidelity, gratitude, and desert.
We cannot argue that its recommendations are inferior to those of an
alternative normative theory without knowing what the specific recommendations of each theory would turn out to be. Fictional counter-examples
that simply stipulate what maximizes utility do not show that RU yields
unacceptable results in the real world for which, presumably, normative
ethical theories are intended. Actual or realistic counter-examples, however,
are always controversial because it is uncertain what the long-term consequences of various complex sets of rules would be. (Hill: 164.)
I am not sure that mere departure from ordinary moral thinking makes RU arbitrary but the key point is that at the current level of discussion RU is schematic. We don't know what rules it would licence, a fortiori we do not know if and to what extent they would depart from ordinary moral thinking.
Second charge of arbitrariness
This is the objection which your question poses. It is that RU rules become so overloaded with qualifications that the situations to which its rules relate are so specific that RU becomes de facto indistinguishable from AU. But you omit a key point. There is every reason why RU should not incorporate densely complex qualifications. Remember a consideration from above :
The rules are taken to be public, teachable, socially reinforced
rules that should be internalized by all. Such rules may include "built-in"
standard exceptions, but they would not be useful if they were too complex.
The ever-more qualified rules you conjecture would be too complex to guide practical reasoning. AU aims at total finesse, at the exactly best outcome in every individual situation. RU lowers its sights and in my view becomes more reasonable and realistic in doing so. The aim is to formulate rules the general acceptance of which by
most people in the relevant community produces at least as much utility as
such general acceptance of any alternative moral code: and the calculation of utility can from the nature of the case be only approximate given our fallible judgement and imperfect information, the very limitations which make AU impracticable.
Endnote on AU and rules
Some act-utilitarians deny that the AU principle should be used as a
working guide to moral decision-making. Instead, they treat it as stating
what would make agents' acts objectively right even if the agents could not
know what is objectively right, should not even try to discern it by estimating utility in the particular case, and are often utterly blameless in failing to
do it. Such utilitarians can consistently recommend following rules the
general acceptance of which would apparently maximize expected utility,
but they can only recommend this as a useful heuristic guide likely to result
in right action more often than trying to estimate utilities in particular cases.
Sometimes, AU must concede, following such rules may lead to wrong acts
because what maximizes utility (and so by AU is objectively right) in the
particular case is not always what is prescribed by rules the general acceptance of which would maximize utility. (Hill: 162.)
So AU can find a place for rules and allow that in certain circumstances it is best to follow them. But it cannot argue that following rules all or most of the time is the best way to go about things - otherwise it loses its distinctiveness and collapses into RU.
Reference
Thomas E. Hill, Jr., 'Assessing Moral Rules: Utilitarian and Kantian Perspectives', Philosophical Issues, Vol. 15, Normativity (2005), pp. 158-178.