Doctor: Easy! I’ll hook myself up to the computer! She can borrow my memory space!

River: Difficult! It’ll kill you stone dead!

Doctor: Yeeees, easy to criticize-

River: You’ll burn up both your hearts! And don’t think you’ll regenerate!

Doctor: I’ll try my hardest not to die. Honestly, it’s my main thing.

So, River knew she wouldn’t regenerate either! Moffat’s clever way of making the Doctor the only one who can regenerate.