The CFI doesn't need to be "Checked out"
Hi Jim,
If you're a licensed pilot and taking a BFR, since you're the PIC, the CFI doesn't need to be RV qualified.
I recently renewed my CFI and the examiner isn't RV-10 checked out.
He did, however, put me under the hood..(foggles) and did some whoop-de-doops that I had to recover from. It doesn't take any particular airplane checkout to do these maneuvers in an airplane that you've never flown before.
As to your earlier question, it depends who's answering...a CFI or private pilot?
As a CFI, I give local flight instruction occasionally...my preference is cross-country by far...I spray daily, locally, so that doesn't light my fuse, since I have 42 years here and have seen all that there is to see locally by means of my work.
Best,