Anya's decision to break the time paradox.

The fact there are wormholes all over the places that Sgt. Cortez visit, must mean that the original timeline was broken each and everytime in order for that version of Cortez to give the past version of himself whatever item, advice and help he needs.

For instance:
In 'Scotland The Brave' when Sgt Cortez first went there, he must have ran out of time because he couldn't find the key needed to access the rest of the castle. Eventually finding the key but realising the island was about to be destroyed, HIS Anya probably suggested going back in time to give the key to himself.

That is the only way that Cortez could have originally found a key, or a ghost gun or hacked those terminal passwords.

So when we experience *our* timeline Anya suggesting that it could be risky to send Cortez back to defeat SplitterCrow, it must have been on her mind all the time that it wasn't all THAT risky if alternate reality versions of herself did it multiple times.

This also means that we don't play as the final Cortez throughout the game, but the one before last. The last Cortez being the one that runs into himself whilst still having the R-110 as his sidekick. We then see the cutscene of THAT cortez (because he still has R-110) instead of the one we play as in the final mission. Though if the Time Crystals were indeed destroyed by both of them, when they both tell Anya to get them out of there, they should both go back to their own respective universes with the splitters destroyed, just our Cortez lacking a robot.
When I first watched the cutscene I thought it was cheesy that two Cortez's ended up just as one, but the way I've explained time travel theory in regard to parallel universes, explains this. ;)

/essay