Summary of LA's so-called BRT: They painted the buses red, in the hope that this would somehow make them go faster. Marketing is great and all, but what matters is actually improving service. A lot of the marketing around BRT, in fact, is just trying to disguise the bus as a train. I don't think it works very well. Why not just build a train in the first place?
Cos it's cheaper not to...
It seems to me that if you do it properly (set aside dedicated roadspace, create proper stations) you can create bus service that is just like a train, and then the only marketing you need is to let people know about it so they try it, and the service should speak for itself.

The alternative, as you mention, is to try to use the force of marketing to put a sheen on normal bus service and sort of wish it into being seen as BRT.  I certainly do hope that isn't what ends up happening here in NYC.

Except it's not a train. It's got rubber tires. The vehicles are small and cramped. The ride is less comfortable. It probably runs on the street at some point. And if you spend enough money to build a "train-like" BRT, it's basically the same cost as building a train in the first place, only trains have significantly lower operation and maintenance costs, since rails last longer than pavement, and one driver can drive a single bus, or an arbitrarily long train. Also, one thing that "proper" BRT does, with its dedicated busway, is internalize the road maintenance costs to the transportation agency, rather than having them disappear into the general road maintenance budget. On the whole, not a very good deal for the transportation agency.