It's quite probable that case design is one of the sound-reflective surfaces that is exacerbating this problem, but the problem is NOT a iphone case issue alone.
If it were, there would be a simple way to test it:
- Remove the phone case
- See if the problem persists
... which it does in several anecdotal tests we have run here.
We have had some succcesses by altering the position used to hold the phone - echoes off the surface of a hand holding the phone at the base seem to be a factor, or echoes from laying the phone flat on a surface (likely two of the more common methods of speaking on a smartphone).
One solution has been to manually hold the phone elevated in the air with the bottom of the phone pointed skyward, and speaking into it that way. Far from a utilitarian solution.
The closest I have found to a more practical solution has already been posted here - to manually close all other apps while on the phone. In several of our tests, this has resolved the problem.
This is just my opinion, but I am convinced this is an inherent design flaw built into the 11 (non-Pro) series.