Yes, of course you are 100% correct.
This only masks the problem from the end user. But after deleting all the other plugins, dumbing down the theme to twenty twelve, etc., I simply ran out of time. I’ll continue to test potential fixes on a test site and post my results here.
Note that I tested the form and intentionally created errors (not filling out required fields, etc). When there is an error, the replacement ajax-loader.gif displays for a fraction of a second before Contact Form 7’s error message appears. I’ll have to edit the gif to make it an animated gif with a 1 or 2-second pause.
I don’t recommend that anyone does this unless you’re certain that the emails are actually being sent properly.
