For example, your app icon would be blue and black and your logo on printed shirts would be red and black.
BRANDING IS NO A BLACK AND WHITE FIELD. iT IS ART AND SCIENCE. You need experience, as I have after more than 30 years serving small to large brands
The idea of a fixed color for a logo is valid for medium or large size corporations. A start up may be smart and client focused.
The logo color is an instrument to talk to the customer heart. As long as it is consistent and planned in advance, a logo may have a color palette (an expessive one) and use it according to diferent audience. There is exempoles of Fortune 500s logo that follows such policy, for exemple: Apple, Citi, Coca Cola, Yahoo, Googlr.
This is what I call the Camaleon Law. In America, use red and blue, in Brasil, yellow and green, and so on.
I will be very happy to give you insight about how to build an effective brand identity.