After about an hour of searching, I strongly suspect that this is a case of abuse of power by a misguided TSA employee acting outside his authority, though I have not been able to convince myself of that fact, and so the normal disclaimers about nothing on this blog being legal advice should go at least double for this post.
The reason I strongly suspect that this is a case of abuse of power by a misguided TSA employee acting outside his authority is that the regulations on penalties and prohibitions mostly focus on making sure that you can't get certain things into secure areas. For example, 49 C.F.R. 1540.107 says that no one can enter the sterile area or board an aircraft without going through a screening. However, in this case, the putative flyer wasn't trying to get into the sterile area or an aircraft without going through a screening - he made a conscious decision to avoid a screening by not entering the sterile area or boarding an aircraft. Similarly, 49 C.F.R. 1540.109 prohibits threatening, interfering with, assaulting or intimidating screening personnel. However, in this case, the putative flyer wasn't interfering at all. Indeed, the screening personnel could have done their jobs more easily if they had simply let him leave the airport. Because there is no evidence that leaving the airport had any adverse effect on security, or on the ability of the screening personnel to screen other passengers, it seems to fall outside of the general scope of the regulations, and so I suspect that the threat of a $10,000 civil penalty was not supported by law.
However, the reason I haven't been able to convince myself of the fact that a civil penalty couldn't have been imposed is that the relevant law is more than a little bit difficult to wade through, and the regs have previously been applied in ways that seem patently unjust. In terms of difficulty wading through the regs, I will give one example: 49 U.S.C. 46301(a)(5):
(A) An individual (except an airman serving as an airman) or small business concern is liable to the Government for a civil penalty of not more than $10,000 for violating—
(i) chapter 401 (except sections 40103 (a) and (d), 40105, 40106 (b), 40116, and 40117), section 44502 (b) or (c), chapter 447section 44502 (b) or (c), chapter 447 (except sections 44717–44723), or chapter 449 (except sections 44902, 44903 (d), 44904, and 44907–44909) of this title; or
(ii) a regulation prescribed or order issued under any provision to which clause (i) applies.
And that's just one example. As a lawyer, I can wade through that, cross checking sections, examining applicability to a given situation, etc. However, as a human being, I don't do that sort of thing for fun, and no one is paying me to write this blog. In terms of unjust application of the regs in the past, I refer readers to Rendon v. TSA an unhappy case where a civil fine imposed for asking some rather profane (but not unreasonable) questions about security procedures was upheld under the prohibition on interfering with screening personnel. While I think imposing a fine for trying to leave an airport is even worse than the situation in Rendon, given the result in Rendon, it wouldn't surprise me terribly if a fine, in fact, were imposed.
So what will happen in this particular case? Probably nothing. I doubt the TSA will seek penalties, given that the whole incident was video taped, and a trial would only lead to bad press and the possibility of their powers being curtailed. In the end, my guess is the whole thing will blow over, the TSA will keep their current security policies in place, and most people (e.g., me) who can't afford to skip flights just because we might not want to be molested by the TSA will end up being subjected to whatever form of invasive screening the TSA thinks is warranted without any realistic avenue for recourse.