Can anyone give them a call tomorrow and ask just to make sure I'm getting a straight answer?
I wouldn't suggest calling. You won't have any tangible documentation of the answer. You'll need it if you get conflicting information along the way.
It has been my experience that you often call 5 times, ask the same question to 5 different people and get 5 different answers. When you have something in writing, there isn't room to argue that you weren't told something or you misunderstood.
What I would do is email WDW (wdw.college.recruiting@disney.com) and also DLR (dlr.college.recruiting@disney.com).
You should get the same answer.
But if you don't, then you should forward each of them the answer that the other provided and ask them to get a definitive answer.
If they both say that you can (first try or after several), then you have that documented. If you run into someone further in the process, like during your interview, that says "no", then you have the documentation that says that you are OK.
With that said, my opinion is that you really should pick which program you want to apply for and leave it at that. Outside of the name and basic "living, learning, and earning" concept, they are very, very different (costs, classes, housing, transportation - DLR doesn't have it, available positions, etc.) They paint the picture that the only difference is that one is in CA and one is in FL, but there are more differences than just location. A lot more.