Some labs hire "research assistants" to do technical work in the lab, not any actual "research".
I have heard of a few profs who allow their thesis students to come up with their own project, as well as a few profs who don't have undergrads working under the supervision of a grad student, but in most cases you'll be given a project that's an offshoot of what a grad student is doing, or directly a part of the grad student's project.
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