The point is that the "how" he got the stealth is flavor.So, then, if the character is deprived of his assumed stealth boots and black face paint, he'd suffer a -5 penalty to Stealth checks?
The notion of training comes with knowledge, and that knowledge can be translated as having the right tools and equipment.
I.e. a rogue who rolls his thievery to disable a trap could be described as either have stick a twig in the gear, a precise tool he carries with him, or his dagger, it's irrelevant. If he'st he type to have a 'tool for every job', then he's got them, you just handwave it as part of the skill.
To put it another way:
I've never heard of a DM penalizing a fighter for not specifying that he was sharpening his sword, or repairing/oiling his armor in between fights, or doing anything to address this. That is just handwaved as "What a fighter does to maintain his gear" without making the player account for it by allocating time or funds to whetstones/armor repair kits. So, to me that is no different than "what a thief does to be stealthy".
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