Negative XPDR - under the outer ring of Class C

I fly a an "aircraft which was not originally certificated
with an engine-driven electrical system" under 91.215. I
have no transponder, but do carry a handheld radio. I was
recently told by an FAA designated pilot examiner that I
cannot fly under the outer ring of the local class C
airspace. I know I can't enter the class C. I can't find
anything in 91.215 (or elsewhere) that says I can't fly
under the outer ring of a class C.

91.215(b)(1) says I can't fly into the class C (or any A or
B)

91.215(b)(2 and (3) ) apply only to 30nm Mode C veil ops
(not applicable here) and say I have to stay below the top
of the class C or B (or 10K' if lower) when inside a veil.

91.215(b)(4) says I have to stay over 10K' if overflying the
class C and there's no mode C veil.

91.215(b)(5) doesn't apply.

Am I missing something or is he wrong? It looks like I can
fly under Class B or C airspace even when there is a mode C
veil.