Capturing the AI is hilariously easy, especially for a syndicate agent. I can give an absurd list of simple ways to capture one from its satellite.
If you don't want it blurting everywhere about its presence to borgs, you can always subvert it or fly into space for a time.
You also don't have to capture it the moment the round starts either--especially paired with a well made freeform/ hacked law, you have plenty of time to storm the satellite. It's a very rare round that the satellite is so much as given a single door as an upgrade to its meager defenses.
The objective isn't meant to be easy in the slightest, as you're stealing a giant station element. This isn't akin to stealing a positronic brain.
This isn't even beginning to talk about the ability to create a new AI, which is trivial for roles such as a scientist or engineer.