The quantum computer idea was literally invented by David Deutsche to test the many universes theory of quantum physics.
"Do quantum computing folks really think that we are borrowing capacity from other universes for these calculations?"
In this context, your opinion and Deutsch's opinion don't matter. The question is about whether the idea is common in the field or not.
Quantum mechanics is a tool to calculate observable values, and this tool works very successfully without needing to make strong assumptions about the nature of the universe.