Saying that if it happens you surface right now or you drown is being way too melodramatic.
Obviously, from observing it on a boat you now know how long it took to empty on the surface, and it would take about half that long to dump a tank that was half full underwater as it is a fairly linear equation. That is more than enough time time to do a swimming ascent (assuming you are not in an overhead environment) or to connect with a buddy and share gas.
More importantly, it would be very rare for the failure to occur underwater after the pressure has dropped significantly from the fill pressure. The vast majority of burst disc failures occur during the fill, and most of the rest occur while the tank is sitting around with a full fill. It is rare to have a burst disc rupture during the dive.
A burst disc is designed to rupture at between 90% and 100% of the tank's test pressure. For a 3AL or 3AA tank, the test pressure is 5/3rds of the service pressure stamped on the tank. So for a 3000 psi 3AL tank, the test pressure is 5000 psi and the burst disc must rupture at between 4500 and 5000 psi.
What this means is that unless the burst disc is corroded, it is not going to fail at anywhere near the normal service pressure, even if the tank is painted black and is sitting in the sun in the middle of the sahara.
Burst discs should be, at a minimum, changed every time the tank itself is hydro tested. That ensures they get replaced every 5 years. Rinsing the tank and valve thoroughly after each salt water dive will hep prevent corrosion.
With tanks that are frequently used in salt water (rental tanks, etc) replacing the burst disc every couple years is a good idea. Tracking rental tanks is not hard in this regard - if the serial number ends in an odd digit, change it at the VIP in odd number years, if the serial number ends in an even digit, change it at the VIP in every even numbered year.
Consider it to be something that should be done on a regular interval whether it needs it or not - like getting your reserve chute repacked every 180 days.