I can say that he's certainly using a 'step up' 5V to 12V transformer with stated output of 12V at 1A current which is what's required for his 276C but it shouldn't short anything behind the ciggy socket regardless. There is always the possibility that the true output current of the transformer is really somewhat less than 1A or isn't properly smoothed as is sometime the case with cheap imported electronics and the Garmin speaker/psu might have some cut-off protection against that.

I'd be checking the actual power and current output of the adapter with a multimeter if the Garmin cable's fuse is shown to be ok.