The problem here in not appearing incompetent, but being wrong/confused. This is the problem that should be fixed by reading the literature. It is more efficient to fix it by reading the literature rather than by engaging in a discussion, even given good intentions. Fixing the appearances might change the attitude of other people towards preferring the option of discussion, but I don't think the attitude should change on that basis, reading the literature is still more efficient, so fixing appearances would mislead rather than help.

(I use parentheticals to indicate that an observation doesn't work as a natural element of the preceding conversation, but instead raises a separate point that is more of a one-off, probably not worthy of further discussion.)