Echoing what others have said, if they let you, take a set of vitals, if they don't want you touching them at all, simply document that.
As far as gear, go ahead and just grab your first in bag for all calls automatically. Better to have it and not need it then need it and not have it. If your partner is questioning you why your grabbing it for your "obviously" BS call just tell him/her that. I've been on the run that was dispatched as a minor fall only to find an unconscious/unresponsive patient with a respiratory rate of 6 and diminished tidal volume. Not exactly a call I would want to walk in with just a gurney and nothing else.
For us, if we arrive on scene first or at the same time as the paramedic engine company, we'll bring in the gurney, BLS bag (that contains both airway and trauma supplies) and the Zoll, while the FF/medics on the engine grab their drug box. If the engine is on scene first, they'll grab their Zoll and drug box and a small airway bag and we'll bring in the BLS bag when we get on scene, unless the engine radios us with specific equipment requests (gurney only, c-spine, etc).