Right, this is the quote I suspected you were referring to.
When Mexico sends its people they’re not sending their best. They’re not sending you; they’re not sending you. They’re sending people that have lots of problems, and they’re bringing those problems with us. They’re bringing drugs. They’re bringing crime. They’re rapists, and some, I assume, are good people. But I speak to border guards and they tell us what we’re getting.
Anyone being honest with themselves would, after reading this quote, understand what Trump meant. He stated that people coming across the border are bringing drugs and crime. They're rapists - not all, but there are rapists and criminals in the bunch. Some are good people. And border guards confirm this is what is happening.
Sure, if you wanted to take his comments absolutely literally without any chance of possibility of any other meaning, you could probably fall back on your interpretation. But conversation and nuance is a part of life, and if you were being honest and not sick with TDS then you'd get that.
I don't find any fault with most of what you said. Though I'd point out that those being used as "pawns" in the argument are being used as such by both sides of the political spectrum.