I don't know why your examples of sheltered upbringing are all modern ones.Since I fail to see any relation between protective parenting and the things covered by the INT stat, I'll reply to several possibilities.
Hypothesis A: you meant that sheltered upbringing was detrimental to the INT stat and thus part of the explanation of the 6 INT, not only education level.
I'd say that at most it would, at most, explain low WIS, because I don't see how this aspect has any bearing over reasoning, ability to recall facts, logic or education. It illustrate the differing expectations: you'd say think that you're making a character fitting to a stat value since you integrated "sheltered upbringing" to the DM into your background and didn't explain what link you saw there, while he saw none. It illustrate perfectly my point about different expectations.
Hypothesis B : since sheltered childhood evokes staying in a bedroom reading books instead of doing dangerous things like climbing up a tree with other children, you meant that the PC was smart and knowledgeable thank to his self-taught education through bookreading instead of getting a "formal" education (but achieved the same through homeschooled education).
In this case, I'd concur with Lanefan about the bad faith. It's like having a dump stat and trying to mitigate the discomfort of it by ruleslawyering around the meaning of formal education.
Hypothesis C : you meant something else
In this case, feel free to use words to convey your meaning. Just bolding a part of your previous answer didn't help me to understand your point.
You were suggesting that a low Int character should not know basic facts about society. "I was brought up in a log cabin in the woods and didn't meet another person until I was 16" would pretty much cover that don't you think?
Look I can kind of see how this may be gamed around if a player tries to say they are sheltered and have no education, but then the player has them spouting facts about the setting whener it's convenient. But that's basically covered by not being a dick. You've established in the game your character wouldn't know this stuff. (And if the player suggests that the party go to Candlekeep to research some answer to a mystery it would be entirely within the GM's remit to ask them for a History roll to see if they've heard of Candlekeep).
What I'm really talking about here is the low Int character not having to sit out of planning an ambush or solving a puzzle because their character is supposedly too stupid to participate except by making 'comically' bad suggestions. There are better approaches.
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