Why does that make you livid? Did you think you don't have to obey any laws simply because you're at a border? I guarantee you it's still a felony to murder someone there, so why would lying to a federal agent be any different?
Because the purpose of law is to protect people. The purpose of murder laws is to protect people from the act of murder. The purpose of constitutional law is to protect people from tyranny.
I don't understand what point you're trying to make. My point is that you can't reasonably claim that all laws go out the window just because some constitutional protections are suspended. Saying that it should be legal to lie to a federal agent under those circumstances is roughly equivalent to saying it should be legal to murder said federal agent under those circumstances (which is obviously not true).
The only other conclusion is that you think that the law against making false statements is somehow special and it alone should be thrown out under those circumstances. But there's no reason why that particular law should be special, so the much more straightforward assumption is that you think laws in general shouldn't apply in those circumstances.