Not a myth. This isn't strictly grad school related, but last summer I was rejected from a very prestigious undergraduate internship at Harvard (of all places) because I was overqualified. I shit you not. Here's the email I got:
Dear XXXXXX,
Thank you for application for our summer internship program. We were quite impressed with your background and experiences, and actually considered you to be over-qualified for this particular kind of administrative internship. I am writing to let you know that your application, though exceptionally strong, will not be considered moving forward.
....
We are very excited about the synergies between your work and ours, including your work with Dr. XXX, and we know that there will be a fantastic opportunity to link them together.
...
We hope that you will continue to stay in touch with us, and that you feel equally eager to find a way to engage together. Again, thank you for everything - your availability, your flexibility, your imagination, and your desire to be part of the XXXXX. We look forward to more in the future."
I'm sure you all can imagine how much I freaked out when I read this....I mean, WHAT. Makes zero sense. Zero. Did they think they were doing me a favor? I guess I'll never know.