Search results shows deleted people

Symptoms;You synchronize with AD, you get new people in your Profile Database.
You delete someone in AD and expect it to be removed from the profile database at the next scheduled sync. This is what append.

You search the name of the deleted person and you still see it in your search results.
My theory is that when SPS index the database for the people, it does not use the Profiles DB to retrieve the users. In fact, the engine is indexing the Public Side of “My Site". Yes. Even if the user never “created” his own “MY Site” the public side is existing. The user only create the personal side of “My Site".

The “My Site"s are not synchronized with AD during the Profile maintenance.

The sites that are obsolete are deleted only after 90 days (or whatever).

So, in my own knowledge, to have something automated, I would need to create my own updater to remove the obsolete sites everyday.

I would love to ear opinions about this.