Is this a 'home inspector' or someone associated with actual code enforcement?
This is the primary question. If this person is an actual AHJ, then point out that there is no NEC requirement for the plug-in tester. None whatsoever, full stop. If there is some local amendment requiring this, then someone should fight that issue, because it is going to cause almost EVERY home built before 1974 to require FULL REWIRING.
The requirement for a GEC was added in 1971, with full implementation required by 1974. So if the house was built prior to that full enforcement requirement and does not have EGCs in the wiring method, it would have PASSED CODE at that time and is thereby “grandfathered” in so long as not altered or added to.
If this person is a realtor prescribed transaction contractor or just someone requested by a homeowner, he is a nincompoop and needs education per the above. He cannot require that a house be fully rewired. It’s also something you can ignore in your job, so long as YOU followed Code requirements. In other words in this situation, YOU are the legal Code enforcement authority (assuming you are licensed).
Just so you know however, PART of the Code allowance for using a GFCI in lieu of an EGC (NEC Article 406.4(D)(2)) is that ALL outlets must be LABELED stating that there is “No Equipment Ground”. Most GFCI receptacles come with that label in the package. If you do it with a GFCI breaker, or have one master GFCI receptacle protecting multiple outlets, you need to make and apply your own labels.
Final edit: if the house WAS built after 1974 and has EGCs, but the ground connection is BROKEN somewhere, then that is a different issue that must be addressed. Also, if you ADDED ON to an existing ungrounded circuit as part of NEW PERMITTED CONSTRUCTION, then you screwed up. You would have needed a new Hone Run with an EGC back to the panel and ground bar.