`flyspell-prog-mode' uses the original M-TAB binding outside of
comments, which is nice (see bug#18533). However, it doesn't account
for remapped commands. For example, I remap `completion-at-point' to
`company-complete' when `company-mode' is active. If I hit M-TAB while
`company-mode' and `flyspell-prog-mode' are active, I get
`completion-at-point', which isn't what I want.

To reproduce this issue, you can do the following:

  emacs -Q
  (global-set-key [remap completion-at-point]
                  (lambda () (interactive) (message "remapped")))
  M-x flyspell-prog-mode
  M-TAB ;; Or C-M-i

I've attached a patch that fixes the issue (hopefully it works in all
cases; it works for me).