I don't think a lot of undergraduate research students engage in "independent experimental thought." Of course, if you're working with something very expendable, like yeast, you might design some experiments etc. that your PI would just review, but if you don't like things like yeast and bacteria, why torture yourself?
The more important thing is understanding the broader picture. Know the history of the field, the current most pressing questions, the future applications of the knowledge people are trying to gain. If you understand and can articulate these things well, you will do fine during the MSTP admissions process, which is what I assume you are worrying about.
