I'm sure there's no hard "evidence" in the sense of a college administrator on video saying, "Gosh, I love these international students because they let us charge more!"
But it's just how prices work. If you're selling widgets for $5 each, and a new batch of customers come along who are willing to pay $10 for a widget, guess what your per-widget price is now. If you can't sell them all for $10, you might put the rest on sale for $5, but only after you've served all the $10 customers.
The universities are still taking some domestic and/or scholarship students too, but they're naturally giving preference to the full-paying ones.
Could there be other factors driving up tuition? Maybe, but student loans have been around for a long time, and I don't know that they've gotten a lot easier to get. Maybe the recent talk about student loan forgiveness has made some people more casual about taking on debt, assuming it will be forgiven, but that's questionable. The growth in international student enrollment is the one big obvious change.