I've flown these a few times and asked myself the same question.
Torino seem quite happy if you tell them you are climbing to 10,000' as soon as you enter the valley (Val Susa or Val d'Aosta). Like you, I've taken it to mean separation from ground as defined for IFR (i.e. within 10nm).
You're pretty unlikely to encounter IFR traffic below FL100 near the Alps, and chances are you'll lose VHF reception for part of the crossing anyway.
It'd be interesting to know the strict definition.