Yes you are 100% right.
However it still remains that a top ranking page will show in a personal search if relevance is confirmed.
Let's look at your fictional example.
If my page got a #1 for Abortion and it dealt with emotional advice and it turned up #1 for someone searching for legal advice, it would get a high bounce rate.
It does not matter if personal skews the results based on topic preference, the results outside the desired niche are not relevant.
When I search using a proxy, if my term turns up in #1, it will also be #1 in a personalized search.