"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated"
Also, you can work with more than one head hunter at a time; there's no reason to work with only one. If the lying one keeps getting you good interviews, then ask him not to "fix" your resume, but I wouldn't worry about it too much.
That being said, there are plenty of headhunters that do what I call "marking their territory." A lot of companies maintain a database of potential candidates and their resumes. If and when you get a position, they pay the headhunter who found you, but oftentimes they will pay whoever put you into the system first. So, headhunters will scour job boards and tell you about wonderful positions they've found and how they have a really good relationship with the hiring manager (who they don't know) and ask you if you're OK with them talking to company. When you agree, they simply submit your resume to the companies candidate database. Other recruiters will know this and will therefore have no incentive to work with you. If you are in need of a job or you might have liked it anyway, everyone wins, but most of the time it's just a way to squeeze their competition and it can really screw you because plenty of companies won't "expire" the candidate entry for a year or two. When you need a job down the road a little, recruiters won't work with you because someone else has basically excluded you (for their purposes) from a number of good places.
If you suspect your headhunter may be doing this, then tell them sternly that you do not permit them to submit your resume anymore ANYWHERE.
This reminds me of the way orchestra auditions have changed over time (described in "Blink"). Before, candidates would play in front of the judges and the judges would decide-- seems harmless enough. However, women have been consistently under-represented in orchestras, and especially on instruments deemed "better" for men (e.g. french horn). Now, candidates perform behind a curtain, so that the judges can't see the candidates, only hear them. Almost overnight, the number of women skyrocketed. I think it's essentially the same thing with women in math and science. People are predisposed to think that men are better than women at certain tasks/professions (even if it's subconscious) and this is reflected in the number of women we see in various industries. I don't think anyone is really immune from this, and in math and science, I think the framing effect is rather strong. Just read some of the blogs of women in science (e.g. http://scienceblogs.com/isisthescientist/) and you'll see that there is still an opportunity gap.
Also, it's not entirely the fault of men. I think women have almost just as much to do with the problem. From mothers telling their daughters they're not smart enough to do science to an example from aforementioned blog: Isis took her toddler to daycare and the caretaker asked what she did; she said "I work at the hospital" and the response was "oh, a lot of the other mommies are nurses too." This does not help the problem...
I'm not sure I get what you mean by "truth". As the GP said, physics is about making useful predictions within constraints. Under whatever definition of truth you choose to use (it's hard to tell from your post), it would inherently require contradictions to abound. I certainly don't like any definition that allows us to derive contradictions, since that means we can derive anything, which is certainly pretty useless.
One of the biggest advances in scientific thinking in the 20th century is Popper's analysis of falsification and that induction doesn't exist (or at least doesn't really work). Philosophers have struggled for centuries to come to some understanding regarding when induction works and when it doesn't. Not letting scientific theories ever be "true" solved a LOT of problems, since once you prove something true, it can never be false-- and this isn't just a cop out; from a logical standpoint, proving something true and falsifying it are asymmetrical. To prove something true requires you to show validity for an infinite set of cases, whereas falsification only requires you to find one counterexample, and this is why designing experiments that can potentially falsify your theory is so useful (and also why string theory is criticized for not predicting anything that can be tested). Scientists have moved away from the old definition of truth (as you seem to understand it) for good reason.