You're correct. If a team fouls and would get an unfair advantage, the game clock can be started or stopped at the discretion of the R. Taking a DOG definitely falls into that. My general rule for myself is any presnap foul qualifies, especially if the play clock is low since they will get a fresh 25 after enforcement. If Team B is winning, I would restart the clock like normal. Team A is working against the clock on that situation, so restarting it actually hurts them anyway.
As a bit of a retort, ask your colleague how many times he would let Team A take DOGs to run out the clock. Say Team A has 1st and Goal with 4 minutes left and continually lets the play clock run out. How long would he let it continue before putting an end to that farce?