Again, I'll start out by saying I have no idea if the flyers tried to move Frost, and in general, I have no idea if DiMarco is telling the truth. Even if we believe this to be true, I don't think we know the value for which the Flyers were asking for Frost. Where they asking for a multiple picks, a 1st rounder, an A+ prospect? So this conversation is very much a conceptual conversation (which goes along with your first paragraph).
By not playing Frost, the Flyers are basically showing their hand. If Frost was perceived as valuable as Brink, or Foerster (for example), he would play as much as those players**. So sure, I can agree that sitting Frost might not reduce other team's perception of Frost's on-ice impact or future potential; however, it illuminates the Flyers internal value of Frost, which isn't high. Therefore, sitting Frost weakens their negotiation position, because it gives other teams the insight into the Flyers evaluations. This isn't a problem if they just want to get a deal done, but it is a problem when you're trying to extract the most value out of a negotiation. You know just as I do, negotiations are not about always about value of the asset. It's about a perceived value from all parties. If other teams know the Flyers don't value Frost, those other teams are not going to offer as much.
**Of course this assumes that there is a normal power hierarchy, which doesn't appear to be. This also is not helpful in negotiations**
When it comes to Dubois, it's not remotely the same type of scenario. Dubois had (basically) two 50 point seasons, and one 60 point season (as a 19, 20 and 21 year old) before asking for a trade. He then put up two 60 point seasons, and asked for another trade. Frost's value is about future potential, and Dubois' value was rooted in previous performance. Teams knew what they were getting when acquiring Dubois.