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.