Singular or plural verb after parenthetical material containing a conjunction?

Two references say the verb should be singular, and I have seen none that say it should be plural.

"Rule 3. Parentheses, despite appearances, are not part of the subject. Example: Joe (and his trusty mutt) was always welcome. If this seems awkward, try rewriting the sentence: Example: Joe (accompanied by his trusty mutt) was always welcome." Grammar Book

"Incorrect: The president (and his assistant) were expected to arrive by 10:00 a.m." The Punctuation Guide

The general rule with parenthetical expressions, is a complete and grammatically correct sentence, when the expression is removed. Parenthetical expressions are meant to clarify, though they do not change the grammatical structure of the primitive sentence. The use of the conjunction 'and' is incorrect. The verb must precede the expression in order to preserve the grammar. As it is stated in the comments above. Example: 'Sarah has, as do we all, a lot to think about.' Take out the 'as do we all' and the sentence is still complete, and the grammar intact.