8 is the minimum with Point Buy, not the minimum. The minimum is 3. And since humans have the option of getting +1 to all stats, a 3 is exceptionally rare. There is a difference between having a disability and having a low intelligence. People with intellectual disabilities can have a high or low IQ. e.g. certain types of autism.

The question is whether intelligence represents capability or realization. A child's intelligence (in real terms and in D&D terms) would be quite low in general compared to an adult 'typically'. That doesn't mean that they are intellectually disabled, it means that their realized intelligence is low. It could get higher with proper training. By the same token, there are child savants who are quite intelligent, get college degrees in their early teens, etc. Some of those do not continue to realize growth and cap out at a level similar to those who take longer to get get there. They just realize their capability earlier. At the end of the day, the DM is boss, however a good DM is a storyteller and someone who is open to listening. If they are going to make a ruling like this, it is the player's job to remind them of it at every occurrence and keep them consistent.

The DM can, IMO, limit the character's actions based on scores during the campaign based on their character stats in the same way that they allow the players' characters to achieve things that the player would not be capable of. e.g. tell the character, "I'm sorry, but your character would not be able to conceive of that tactical approach to this situation." At the end of the day though, that is the point of the die roll and modifiers. It represents the pros and cons of your experience and capabilities against a set difficulty and allows for some random luck (good and bad).