We run L&S on nearly all responses, particularly since our dispatches are known to be wrong. I've been called to a "teen not feeling well" only to roll up on him in full cardiac arrest! Of course, I've also responded to "pregnant, full-term female hemorrhaging" only to determine, on-scene, epistaxis. The only time we wouldn't go L&S to the scene is if the dispatcher, PD or first responder says, over the air or a recorded line, "precautionary" or "mental hygiene."
From a legal perspective, they called 911 because (they believed) they were having an "emergency". If I were called to the witness stand, I would have to answer why I took it upon myself to determine it wasn't an emergency.
From the scene to the hospital, it just depends on the condition of the Pt. We don't employ hard rules. The notion you wouldn't go L&S with BLS is crazy. In NYC, as in many places, all trauma is BLS. If I have a guy who fell 15-ft off a ladder and is unstable or potentially unstable, you won't find me stopping at red lights under the false notion that BLS is never emergent.