No they don't, the whole reason for Homomorphic encryption is sending stuff out of your device.
You don't need any encryption to process locally.
The erroneous claim was that Apple handles image recognition and image search on servers, the way Google does.
Apple handles those tasks on the users own device(s) for privacy reasons.
I don't think anyone made that claim in this thread.
They do handle image recognition (at least some aspects of it) on their servers, unless you specifically went and disabled the right setting: https://news.ycombinator.com/item?id=42533685
Sending everything to a server is, however, how Google's service works.