It also puts .gov in a spot concerning other candidates that go to the border. Donald had to know DC would pull something like that. He outsmarted them again.
None of them are going to want to follow his lead, only because he did it first, and he made them all look bad.
Still, you're probably right about the pickle DC will be in if any other candidates want to get a tour of the border by the Border Patrol. At this point, they'd have to do the same thing to Hillary, if she wanted to do it, or the sheer scale of hypocrisy would damage them in the voters' eyes.