Jimenez was traded in the middle of 2011 making $2.8M, was under contract for 2012 at $4.75M, and had options for '13 and '14 for $5.75M and $8M. That's very reasonable for a guy who was 3rd in CY the previous year with multiple good seasons before that, even if he was having a tough first half of 2011. He absolutely fits your criteria.
And, if Colorado knew something about him, that's exactly part of my point. Teams trade guys away when they think their future performance won't be as valuable as the combination of salary relief and talent they'd get in return. If inside knowledge makes them think the guy is going to struggle in the future even if they haven't had many troubles yet, that's a huge part of that equation.
2/$20M is very cheap for a 27 y/o guy a year removed from being the Cy Young Award winner, so Greinke counts, too.
Teams trade away guys when they think the players and salary relief they get in return is more valuable than the performance the guy would give them going forward (which sometimes is because they think the guy is due to regress). Sometimes that doesn't happen until the guy gets really expensive. But sometimes it happens while they are still inexpensive.
They didn't trade him away thinking he'd be good for CLE, they traded him away (and shocked everyone when they did) because they knew he was about to implode and they didn't want to be left holding the bag. That's far different trading someone because you HAVE to, not because you want to trade some youth for youth.
$10m/year is much more like market rate, which is not what we are talking about here, in the direct comparison you'd be comparing Tillman at minimum salary to Grienke at $7.5m.
Garza might have been a closer comp being traded not only at min salary, but at $3.5m and controllable for a couple more years too. The stats are even half way similar to Tillman's over the past year or so (if this is legit). But then again, that's the exception, not the norm, and TB was involved and we know how tight their money is. (Price is a goner this offseason).