Yes. The anomalies absolutely can't be stolen.
But you could lose access to them, if someone else builds an outpost in the system and closes borders to you. Then you'd have to get them to open borders to you, which might force you to go to war with them.
There might also be some edge cases like world cracker or building a ringworld (since that destroys everything but the star in the system). Also, the precurser chains can only be completed by one player. (I've never seen the AI finish them though, so in single player don't worry about it)