You're confusing copyright with trademarks. Trademarks must be defended if you want to keep them (this is logical: if other people are using them, they are no longer a mark of your trade). That doesn't apply to copyright; it's an entirely automatic process.
You are right. Thinking it through you can of course put a restrictive license on stuff that is publicly available, otherwise of course open source would not work. What Adobe may have done is confused their original license terms by posting a download with key, so a court is very unlikely to award more than nominal damages should Adobe get annoyed with it being used, but you are perfectly correct, their copyright still holds up.
