In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase
Neutrino are left-handed. The spin is in the opposite direction of motion.
seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say z-direction. But to not violate Heisenberg's Uncertainty, if I manage to measure Spin in a perpendicular direction of motion, say $S_x$, now helicity must be undetermined. And to be consistent if I subsequently measure $S_z$ (or helicity), I can have the same or the opposite helicity. So, if a measure change helicity (to not to violates Heisenberg), it would be more precise to talk about left-handed neutrinos only in the context of some interaction, without excluding a priori that I can change it's helicity by an accurate measurement of Spin on the perpendicular direction of motion?