They're not being dicks, it's just a subject that comes up too often to take it seriously anymore.
If your biceps fail first during a back exercise, you need to fix it (otherwise sub-par back growth). If your triceps fail first during presses, you need to fix it (otherwise sub-par delt/chest growth).
I'll quote PX here and say "a back exercise is supposed to fatigue...wait for it, the BACK!", not the biceps.
If the biceps/triceps didn't fail, or reach near it...did they get enough stimulation for growth? Why would you train other muscle groups with 100% effort, but not the biceps/triceps?
If the logic of those "don't train arms" people were true, why do intermediate bodybuilders often need to bring up their lagging upper chest (since flat benching hits it too, right?)? Or any other bodypart for that matter? Because tension on that muscle wasn't great enough...
By all means, if you don't want to look like a bodybuilder (with their "cartoon" bodyparts and all lol), don't train them directly. Or if you have the rare genetics to grow evenly with just a handful of lifts, carry on.