I don't think Brightline has to offer Amtrak a slot though correct? Brightline could just say no since they are fully private?
I think I read here that because Florida East Coast RR ended passenger service in the early 1960s and weren't involved in the establishment of Amtrak, they have no obligation to offer slots for Amtrak trains. However, I know Amtrak has talked with them in the past about running trains up to Jacksonville on their line and have even run test trains. Brightline is a slightly different company from FECRR, so I don't know how that plays also.
Call me cynical, but I think that after Brightline makes all the $$$$ from the real estate development around the stations, they'll find that actually running a passenger railroad isn't all that profitable, at least not to the expectations of the capitalist overlords. At that point, we can expect that the Brightline rail service will be shunted over to some sort of public sector operator, maybe even Amtrak!
In any event, it might make sense to make provision to connect Brightline to the national passenger rail system, as much of the ridership on the Silvers comes from points north of Jacksonville and they may want to travel to places served by Brightline and not served by the Silvers. Not only that, if Brightline is really serious about providing Florida corridor rail service (MIA-ORL-TPA, and maybe even MIA-JAX, maybe Amtrak should not bother with trying to start corridor service in Florida and use their funds for other corridors. But that doesn't mean that the Silvers should be cut back. As I wrote two sentences earlier, most of the Silver Service customers are coming from points north of Jacksonville, and forcing everybody to change trains in Jacksonville is sort of silly and would definitely discourage passengers from riding trains to Florida, which a lot of people seem to like doing.