[What do you mean by liver problems? Please give more specifics.
Why not try it? I trust my ND with my life, literally. She has changed my entire life with her treatment protocols. If you find it doesn't work any better, let her know. If she's an ND worth her salt, she'll modify her treatment protocol based on your responses but I think you should at least give it a go.
High Weight: 225
Weight at start of Primal: 189
Current Weight: 174
Goal Weight: 130
Primal Start Date: 11/26/2012
The first time I had ever heard of MCT Oil, it was from one of Mark's Blog Posts....
Also, Dave Asprey promotes the daylights out of MCT Oil (He also sells it, so take it for what it's worth) he writes The Bulletproof Executive blog if you're interested in his perspective
The Bulletproof Executive
Mark has mentioned MCT several places. Just search "MCT". This one in particular...
Dear Mark: MCT Oil, Camelina Oil, and Fancy Canola Oil | Mark's Daily Apple
Personally, if you're primary goal is weight loss (over primal) then maybe try it, but I would go for a whole food myself.