Einstein was much worse in the same department: "You do not really understand something unless you can explain it to your grandmother"!?

That's probably a misquote, it turns out. I can't find any source for it and Wikiquote agrees. The closest they could find was Ronald W. Clark claiming that Louis de Broglie claimed that Einstein believed "that all physical theories, their mathematical expressions apart, ought to lend themselves to so simple a description 'that even a child could understand them.'" (I'm interpreting this to mean that Clark attributed the outer quote to de Broglie, who attributed the inner quote to Einstein while giving his own explanation of the context.) Could be true, but our knowledge of it is a few degrees away from the primary source, so there's room for it to get corrupted or taken out of context along the way. And even if it is correctly attributed and interpreted, the "their mathematical expressions apart" bit redeems it somewhat (not completely). Though that does dilute the meaning of "understand[ing]" as used, or it identifies it with (as you've termed them) verbal understanding rather than technical understanding.

I'm going to tentatively reject the belief that the "...unless you can explain it to your grandmother"/"that even a child could understand them" quotes accurately describe Einstein's belief. He may have been a Traditional Rationalist, but he wasn't stupid, and I imagine he had a great deal of experience explaining things as well as he could but not having everyone (let alone children or stereotypical grandmothers) understand him.

(And I'm going to give myself a rationalist experience point for finding the original "grandmother" quote surprising enough that I thought to look it up.)