I think that is pretty much what the American people always had in mind when they said they wanted “immigration reform.”
Liberals/Democrats, of course, took the words “immigration reform” and twisted them to impose open borders—everything the people do not want—so that they could publically campaign on the issue without actually supporting it.
Liberal/Democrats do this kind of linguistic bait-and-switch all the time. If they ever say they support a popular idea, dig a little—chances are, they’ve stuck its name onto some tired old socialist trope, like a façade hiding the pig pens.
This is why actions speak louder than words. They may say the same phrase, but it means something totally different to them than it means to you.