It’s not just that the possibility of the whole system going down, it’s a question of how robust the entire navigation process is. Just in general we are always on the lookout for miss-matches.
If there is only one source of information there will never be a miss-match.
It’s a mindset. If the weather forecast is for northerly winds and the observed winds are south, a good navigator is going to dig a little deeper.
If the ECDIS holds me in the middle of the river I’m going to have a look to see if that matches the visual picture, buoys, ranges, distance to the bank, what have you.
In the case of the GPS, or anything really the risk matrix is a useful framework :
In the middle of the Pacific I don’t need to worry about GPS failures as much as I do while going up the river.
I know this is well understood, the issue is communicating it to others.