I would imagine that you may be seeing the effect of a lot of techology in one handheld unit. I think that the electronic compass in the Garmin is more suited to overland "Orienteering" than precise marine navigation.
The price of a good fluxgate comapass for one of the modern integrated navigation/information systems is more than the entire 76S! I have a nice Autohelm/Raytheon hand bearing digital compass that is very accurate but was about $150 or so. Add on all the features of the 76S and, well, they had to scrimp somewhere!
Even my two trusty 7" Danforth Constellations, zeroed to within a degree of each other, move whenever ANY ferrous metal or electronic device comes near them.
Just remember that if you turn off your 76S compass, the resulted calculated heading will be over the ground, which means with a beam current, you may be off 10 - 20deg from your magnetic heading. And if you are not moving, you won''t get any heading reading at all.