That is really, really odd. Did they ask you to fill out an accident form? If anything, go to see a doctor on your own, then inform HR and your workers-comp that you want it covered. There is usually no way around this for them.

Essentially, you waiting (which is what they want you to do, I spent too much time around soulless bosses), the injury can get worse and you can be penalized for not "taking initiative" and getting it taken care of. That's how they get out of using their insurance on you, and it's not your fault at all. Go to the ER if it gets worse, don't listen to them and just wait. Especially if they are checking over the phone. God, you can assess a bodily injury involving muscle and tendons over the phone, it had to be examined. How dense of them.