[siegel]

This is not 100% accurate from a trademark perspective, at least with respect to "famous" marks.

Generally speaking, you are correct - unless there is a likelihood of consumer confusion, you are free to use a trademark already used by a senior user.

But marks like Apple and Mickey Mouse, from a trademark, are sufficiently famous that they get special protection. There is a concept called trademark dilution that only applies to sufficiently famous marks. With respect to such marks, a junior user can be liable for use of the mark even if there is no likelihood of confusion.

(BTW: By "senior" user, I means a user that gained trademark rights first and a "junior" user is one that started using the mark in commerce later.)