I'm not sure what your airline friends mean by "TOD". Do they mean leaving the platform altitude on the approach or the true top of descent from cruise. It's essential to always monitor/identify the ADF signal throughout the approach when using it as the primary means of navigation as there are no fail flags with an ADF receiver. Pretty standard SOP for any airline I would have though. Although the 744 has and electronic ident function on the nav displays (it shows the decoded morse), it's still our SOP to listen to the NDB transmission to promptly detect any failure of the aid. I doubt you could properly identify an NDB from a typical jet TOD point as you'd be 100 miles away. Most NDB's only have 10-25 mile range so how your friends airlines imagine they can or should only identify them at TOD is bizarre (and potentially dangerous). If the NDB failed whilst they were tracking it, how would they ever know?
I've never seen NDB errors of 30 degrees. I've only ever seen them waver when there is a local active CB cell. Short term deviations are acceptable particularly when backed up with a moving map display but if there was a deviation of the order you mention for more than a few seconds, I would certainly go around.
To qualify all of this, I'd say 99% of my jet NDB approaches have been in the sim, not the real world, but we still have SOP's that dictate how they should be flown. If they are the primary approach aid, then tolerances (5 degrees) etc must be adhered to regardless of what a GPS generated map tells us. Some pragmatism is allowed in commercial aviation, but not much. Moving maps tell such a compelling story that it would be easy to be sucked in when something was set up wrongly.