Of course, working on someone else’s grant, is what I was referring to. At Caltech, there is the summer SURF program. A student stays in his room, gets funding, and works in a lab. At the end, the student presents his research, or that of his lab, at a poster conference. MIT has January UROP. It is the attitude of the profs that make the difference; they welcome interested students.
I have no first hand experience that is recent, of other colleges. If I was researching Caltech, for example, I could find the high percentage of students applying for a SURF and receiving one. I would want my child to be able to talk to one or two profs, and be accepted into their lab. I would not wish them to be the best to get such an opportunity.
Unfortunately, I only know about these two colleges, and our state schools. In my area, I have pushed for kids to get positions at Scripps Lab. These are paid positions, but extremely helpful for a young person to see if research is the right path for them.