I don't know what time-tested means but mustard oil is banned in EU/US for edible uses due to high erucic acid. So you parents were right!
I've got a bottle of Uncle Roy's cold pressed extra virgin "spicy" mustard seed oil at my local Spar.
The label reads "erucic acid free", so I'm guessing they somehow remove it?
It even has the awful pun of "The healthy Oilternative".
I understand they also remove (most of?) it from Canola Oil.
I don't care either way; let the mustard oil flow. I don't buy the mustard oil thing either. Just don't pretend that mustard oil is somehow healthier than canola. Use whichever fat tastes best to you.