Potential aces are rare and hard to acquire. It seems to me that Chief's idea would make sense for both sides. I would prefer 2/$12 to 3/$24, but I don't think that 3/$24 would be ridiculous.
From Liriano's point of view, there is a risk of injury and a risk of not doing well for the balance of this season. In either of these events, he could end up with much less than 2/$12. Or Liriano could be light out the rest of this season, in which case he would have given up an opportunity to make a lot more.
From the Twins point of view, they might get an ace at a bargain price or they might get another Nick Blackburn type outcome.
This is how deals get made in the business world when there is uncertainty -- both sides meet in the middle based on rational evaluations of their upsides and downsides. Considering the value of an ace (especially on the postseason), it seems like a risk that the Twins should consider. And considering that a shoulder injury could cause Liriano's best offer as a free agent to be 0/$0, he and his agent would be fools not to at least listen.