Well, calling them "lies" is a bit out there, but not entirely incorrect, rationalizations is probably the best way to describe it. The reason it's done is because people where you are from take those jobs at these rates and aside from maybe a different tax burden specific to your country, that's about it.
I don't know the size of the company or how the split is regarding the area you're from and the US/EU but they might have allocated budget to employment counting on this split and not be able to pay for a generalized change, hence why they'd offer if you moved, but offering while being where you are could be "dangerous" as other people in the same position as you might ask for raises as well.
I can't make sense of the "trapping" argument however.
Now, those are the reasons I can see for the policy to be in this way, you are free to disagree, as do I, but the only real answer is going to come from the higher ups. If it's a public company sometimes these kinds of things are listed in their releases with some notes, could be another place to look at.