First of all: this is an excellent question, and deserves a better response than I can give it. I'm far from an expert in Nyingma Buddhism-- among Tibetan traditions, I'm much better read in Gelug texts-- but I'll give it a shot.
The theory of mind that you refer to, that one's thoughts are inaccessible to others, is a mainstay in Western philosophy. A classic explication can be found in Wittgenstein's Beetle Box experiment, and Jacques Derrida (following Levinas's reading of Husserl) has attempted to investigate the ethical implications of the fact that Tout autre est tout autre.
In early Buddhism, the primary soteriological project (and thus Buddhism's raison d'etre) consists largely of the deconstruction of the traditional notion of "self", and the theories of mind proposed are largely subsumed to that project. The "self" is viewed as a collection of five skandhas (heaps, aggregates): form, sensation, perception, mental formations, and consciousness. The relationship between these (and the definition of each term) varies across a number of competing interpretations, but the key factor for our purposes is that each of the above is plural, and represents a flow of discrete events.
In Tibetan Buddhism, this is often conceptualized as a "mind-stream", which is made up of a series of discrete mental events, each of which is linked to the preceding (and succeeding) events (giving the illusion of continuity) by a process of dependent origination. (The fact that a mental event is necessarily caused by a preceding mental event is traditionally given as a proof of rebirth, at least in the Gelug school.) For our purposes, it is important to note that these mental events are necessarily internal: there is no way for someone else to perceive (through ordinary sense perception) these events.
I suppose I should underline that parenthetical qualification; the omniscience of Buddhas (while dwelling in meditative equipoise) is taken as given (and Śāntarakṣita argues this point at length; see Sara McClintock's book on the subject)-- but I assume we are excluding Buddhas here, on practical grounds, at least-- the next Buddha is not expected to arrive in this universe for several billion years, so we can safely table the issue, I think.
Anyway, to return to the matter at hand: the question referred specifically to the Nyingma school, and here we must add some nuance. We have discussed the fact that the "opacity of mind" is near-ubiquitous in both Western philosophy and the Buddhist tradition writ large-- but Nyingma Buddhism is characterized by its (unique) notion of Dzogchen, which is often translated as "radiant mind", and this practice (and the corresponding philosophical interpretations) is the matter of some debate. Nyingmapas (and some Gelugpas) argue that Dzogchen is fully compatible with the Madhyamaka notion of Śūnyatā (Emptiness), but some Gelugpas argue the contrary-- that Dzogchen represents a form of philosophical backsliding which (like some forms of Yogācāra, according to this interpretation) tends toward hypostatization of Mind which opens the way to a reintroduction of Ātman through the back door.
So, to summarize: the "opacity of mind" is not a specifically Nyingma position within Buddhism; in fact, the Nyingma school offers perhaps the best standpoint for an argument against it, if one wished to go down that road (which Buddhists generally don't.)