No. Phony and Antique Sinistea are considered by the game to be entirely separate encounters, so the chance of finding Antique Sinistea is always 1% (except during Sandstorm where it can't be found).

You are imagining the game deciding to spit out Sinistea, *then* deciding whether to make it Antique. That's not what it does. It's 1% of all the possible encounters in the area, not 1% of Sinistea.

The data would be presented differently if the Antique encounter rate were a fraction of Sinistea's total encounter rate.

I'm aware of the context for this question -- the answer is correct, but the percentages it gives are probably not a helpful way to think about the Antique odds.