I was looking through the CBA to try to find something definitive, but I didn't see anything and I don't feel like continuing to poring over a legal document on a Sunday
Let's just speculate since it's easier. Ellis looks at the roster and thinks that the Preds definitely need him to sign, otherwise they are having to find a vet to fill the open RHD role or they will have to hope someone in the pipe line can fill the role. Sitting out of training camp gives him leverage if he's right about the Preds needing him.
Beck, on the other hand, looks at the roster and realizes there aren't that many spots open. He can come in, compete for a spot and maybe even catch the eye of other teams who might be able to use him now. I would bet he is looking for a one way deal. He likely will not get that in Nashville this season, short of having an incredible camp, but he could get it elsewhere. In the meantime, he proves that he is a team-first kind of guy.