You and simonask are speaking at different levels of literality.

Yes, literally, "let's" expands to "let us". But idiomatically, "let's/let us <do this thing>" does not mean "allow us to <do this thing>"; it means "I am requesting that we now <do this thing> together".

Now, I'm not entirely sure why simonask felt this level of literality was a useful one to bring up here, but it is true.

True, but the point was not that they were asking permission, it's the "let us do this together" meaning to which the OP takes offense. He feels like it implies he cannot do it on his own.