I’ve called in several times (2 over the last 3 months most recently), never had pushback.
Quite frankly the last time I called in I didn’t need an extension, it was just a long day with crappy sleep and the hour delay in the second flight was just too much for me. What can I say, I’m a wuss.
Don’t call the DP looking for justification, you have nothing to prove to them and they are not the judge. Their only job is to acknowledge and process your UNfit/Fatigue status. If a DP gives you pushback I’d say “I understand you don’t agree, I am still calling in fatigued.” I would certainly note the DP pushback in the report to ensure the FAA gets eyes on it.