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Not really, your privacy zone is offset (and you can reposition it). But it is true that if you enter your privacy zone during an activity and exit it again (for example, doing 2 loops from home in 1 ride) the middle part of your ride in your privacy zone won't be hidden. And you will have revealed your location/home address.
Also, if your privacy zone isn't really big and you live in a not densely populated place others can pretty much guess your starting point by comparing a few gpx files and the missing distance.
More info: https://www.vrt.be/vrtnws/nl/2022/10/28/strava-kul/
(in Dutch but google translation is pretty acurate)
Also worth noting that if you start your ride safely within your privacy zone, ride down the road out of the area & realise you've forgotten something, ride back & then continue on your ride, you'll have sort of revealed the centre of your privacy zone.