Well, the cartel will want to be the first in that line [to mine a modified protocol].
There is no cartel on the Red Button hard forked protocol. Anyone has equal access to the ability to mine. The fact that someone
was a cartel previously does not grant any vested status in the future. Deepbit, for example, has no greater ability to show up today and be a mining cartel than you or I do.
Come on, you know that "the cartel" there means "the cartel of old-chain miners who want to force a change in the block schedule". It is not "a cartel of rebel-chain miners".
Assuming that "the cartel" wants to kill the value of the rebel chain, it will try to put enough CPU power working on the rebel chain to jam it. That should not be hard at first, because the rebels and opportunistic miners will not all start mining all at once. If the cartel acts quickly, then the rebels who try to use or mine the rebel chain will be frustrated, and (so the cartel hopes) they will give up before others join the rebellion.
Note that, while this struggle is going on in the rebel chain, the cartel's chain (with old protocol except for halving) will operate normally all the time for everybody who upgrades to it, except perhaps for some temporary variation in the block rate.