I think you are reading too much into his response.
The sense I got from that answer was that every piece of fluff they include in monster's description constrains the DM in some fashion.
For example, if the fluff for kobolds says that kobolds are the servitors of dragons, then if the DM wants to use kobolds, she might feel compelled to use dragons (especially a newbie DM). Or she might ignore kobolds because there is no dragon, even though kobolds would have been the ideal enemy to use at a particular point.
That's a 'story burden'. Using kobolds with that piece of fluff burdens the story with a dragon, even if a dragon is not appropriate to the story.
They were trying to minimize those constraints created by fluff. Making the monsters as universally available to all the different campaign settings out there seemed the better option at the time. They may have gone a little overboard, but I don't think the idea was obviously wrong.
That's a bad example because it assumes that labeling kobolds as "servitors of dragons" is good fluff and compounds the problem by assuming if that is the fluff then there must always be a dragon present. Certainly one could imagine all sorts of alternate possibilities where, for instance, a cult of kobolds lived in the sewers of the city and, though never having seen a dragon, sacrificed small pets snatched through sewer grates to some great winged kobold who they hoped would someone day raise them above the station of their misery. (Look for that in the upcoming Creative Mountain Games Narrative Adventure, "Sewers of the Serpent Sect."

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Nevertheless, to address your subsequent points, it doesn't present constraints, it stirs the imagination to think of the creatures in terms of environment, culture, etc. even if what you, as a GM, decides, is different than what is presented in some substantial ways. Flavor text isn't a restraint, it is exemplar, showing typical examples of what is possible as guidance and fodder for GMs.
Too often I see monster entries being used by players as trading cards for what they plan to kill or summon fully expactant that what is presented in the books is the exact mechanical way they will function in-game, in any environment, as to their bidding or to be put up as paper tigers to be killed because they have the books, have read their weaknesses, have done the math, and now will kill and level up.
Look, I am a big fan of wargaming and skirmish games, and played them even before D&D existed, but that style of play is not what roleplaying games are about to me. If all we need are the stats on a card or in a book so we can push minis around a table, with a bare minimum of "flavor" just to pretend one pile of numbers is significantly different from another, I've got better games for that and there's no need to put RPG on the cover.