There is a very large difference between "making rules for science" and "People who are not scientists are telling us how scientific synthesis and analysis should be done."
Do scientists need some form of regulation? Sure. The material covered in courses on medical ethics will let you know exactly how bad things can get when there is no oversight. There's nothing special about scientists that make them above the law, and I've never met one who thinks otherwise (I haven't met Dr. Wagner, but I'm sure she agrees with this too).
In addition, there already is plenty of oversight in what scientists study; a typical process is that an agency declares it is interested in studying "X", scientists write a proposal declaring how they plan to study "X" and if the agency choices the scientist's proposal, they receive funding and begin their study. During the study, periodic updates are given to the funding agency and at the end, the conclusions are written up and sent back to the agency. Typically, the results are also made public in the form of academic publications. In these kinds of projects, the scientists are contracted to do certain work. If they do not fulfill their contract, due either to gross neglect or fraud, the agency can make them repay the funds (although this is extremely rare).
However, this is not what Dr. Wagner is complaining about.
Her complaint is that the scientific community has been collecting data, building models and coming to conclusions about how the world works. However, there has been a strong effort by our current administration to hamper the ability of these scientists to communicate their results to the public. For example, the Strengthening Transparency in Regulatory Science, which on the surface sounds great (who's actually against open science?), has some pretty serious implications, such as not being able to use medical records to help guide regulation related to public health or not being able to use studies whose data is no longer available (very likely to be any study that is over 20 years old, for example) to guide policy.
In short, of course there should be some forms of regulation of science. But this is not what Dr. Wagner is complaining about. She's complaining about silencing scientific research for purely political purposes. It's pretty hard to argue that stifling public health research for political purposes is acceptable (although it's not clear that its entirely new ground).
@FrankHubeny raises a question related to whether one of the laws that Dr. Wagner refers to will be used to suppress the influence on public policy. This is debatable, but clearly we know which side of the argument Dr. Wagner falls on (I personally sit somewhere in the middle: in general open data is good, but the research world is already pushing for this on its own and I'm skeptical about how actual applications of the law would turn out). Given that the question is in regards to whether science should be regulated, not the effect of specific laws on science, I think the answer to given the question is: Yes, scientists should have regulation, just as any citizen should (no murder, etc.). But that is not Dr. Wagner's concern, rather she is worried about suppression of scientific results for political purposes.
@MichealKay asks what is "for political purposes"? I agree this is a slippery slope. If you think climate science is all hog-wash, then it's the right thing to do to be "suppressing" fraud. On the other hand, if you do have faith in the climate scientists, it seems extremely immoral to be suppressing warnings to the public about potential future catastrophes because it might lead to a political opponent receiving more votes.