The "sign-in profile" term should mean only the Incognito profile derived from the initial profile (as per offline discussion with xiyuan@).

However:
* The ProfileHelper::IsSigninProfile function returns true also for the initial profile.
* A bunch of call sites rely on this behavior.
* A bunch of call sites uses the ProfileHelper::GetSigninProfilePath method and essentially do the same sort of check.
* Some of call sites additionally check against the profile being/not being the incognito when they don't want this behavior.
* Some of call sites, presumably, use the IsSigninProfile function wrongfully.

This seems to require some refactoring that would prevent mixing of terms "sign-in profile" and "initial profile".