I wanted to see where it is allowed in the code. You wanted a healthy back and forth. Here we are.

There are lots of things required in the code that are, in my opinion, silly and designed just to make electricians money (AFCI's, for example), so I'm kind of surprised this is actually allowable. Ultimately, decisions are up to my clients, but today, given what I know, I'd try to educate folks to the point they could make their own decision to not move forward with a GFCI "fix".

What would you tell them to educate them?

Speaking of silly codes, I get the safety intent, but a $15k grounded system won't provide any protection for the majority of electrical devices (anything with two pronged plugs). A grounded outlet won't protect your toddler if he/she manages to stick a paperclip in an outlet. Upgrading individual circuits with an upstream GFCI outlet ($40/each) will provide protection from electrocution to your mischievous toddler and to you when using ALL electrical devices (two or three pronged).

Not a bad deal for a "fix", huh?