It seems unusual to me too. Looks to me like he wants to allow the hole to float more in one axis than the other. The hole in one axis forms the C datum. I'm not sure the reference to the C datum in the .08 tolerance makes any sense or adds any information so to me the callout is weird because of that too.
The C datum in the second 0.08 callout establishes rotational positioning of the part. This allows you to 'float' the 0.08 parallel to a line drawn from the center of B to the center of C. They're trying to treat it like a slot- which is probably the exact feature this hole interfaces with. However, the way the print is dimensioned, you will always be restricted by the 0.04 true position anyway. The 0.08" true position is extraneous.
I see what you're saying. It's just that C doesn't exist until the hole exists. So referencing C in the .08 tol seems circular and self-referential.
For machining anyway, inspection not so much.