The decision to check it or not can (and does) depend on the staff member checking you in. The actual decision to allow you in *should* not depend on them. If you get checked, and don't qualify, normally they cannot still let you fly. I know it sometimes happens but that certainly isn't the procedure. The reverse is not possible: qualifying for entry and then getting refused. An airline is of course not allowed to refuse their service to paying customers who qualify for it.
Not sure about the "even" in your sentence. I think it depends only on the person checking you in. Airlines all have the same policy: qualifying for entry is required to be allowed to fly. Quite straightforward.
you could not be more wrong. What is immigrations going to do then? They're not consultants. Agents can give advice, at best. But they want to sell you something and can also not be trusted with anything.
And why do you think nobody in this group gives proper advice? A kid would say: you're living in "upside down world".
define "decide". Whether you can fly or not is defined by rules, which are not in their control. They just need to check. "Determine" could be a more applicable word.
dude 😅. I'm not wrong! Yes it is the responsibility of the airline to check for entry eligibility, but who determines the rules that define entry eligibility? Certainly not the airline.