The person who asks for a check may be protecting work they care about.

Being asked to have your work checked can land as an accusation, particularly if you are good at it and know you are. Usually the request comes from somewhere else entirely: the person is nervous about the thing itself and wants it to survive contact with the world. Caring about the work and trusting you are not in competition. Checks exist because everyone misses things, not because you in particular will.

When someone asks for one, agree without the defensive sentence you were about to add. When you want a check yourself, say why: not because you doubt them, but because this one matters to you.