Paying both would be a very stupid way to spend money as a cap strapped team. I don't think any team, cash strapped or not, should dedicate so much money to two C's that cannot play together. What's the point? It's not like they're contending for a championship and desperately need to maximize the backup C situation. Besides, they are a better team with one or the other + Collins than with both centers. Maybe the answer is that they don't want either C. It's not like that combo has been holding it down on defense.
There are a ton of different ways to address the immediate money issues, but they could kill two birds with one stone by trying to resolve the C situation. If they get lucky and/or play their cards right they might get out of it with more future assets at hand. It's just the ideal type of move to make right now.