Your Stingray 5 should have a ceramic magnet pick up, with a phantom coil underneath to allow hum-free single coil operation.
The 3 way switch should be as you said - bridge position is humbucker, parallel; centre position single coil; neck position humbucker series.
You are correct that the volumes should be similar, although the series can sound a bit louder. I have an 03 SR5 and have had intermittent issues of the sort you describe which have cleared themselves and I put it down to dirt in the switch - it's currently operating fine. Sounds like your tech was wrong about the standard wiring.
2014 Neptune Blue Classic Sabre - roasted maple neck with maple board, mahogany body
2010 SR4 classic collection coral red/birdseye maple neck and board with Flatwounds
2008 Bongo 5HHp lava pearl
2007 SR4HH Blue Dawn LE/rosewood board
2003 SR5H Natural/maple board
1993 SR4 Fretless Sunburst birdseye maple neck
1993 SR4 blueburst with flamed maple neck and board
Markbass LM3/standard 2x10 HF and 2 x 10 Traveller now that's loud!