What systems, in the cabin ceiling, when damaged could cause the masks to deploy?
The scenario where ALL the masks drop, which the article somewhat implies but doesn't outright say, sounds fanciful to me.  A cork striking an individual mask unit might cause that individual unit to drop its masks (so if the unit was for one side of a 3/3 seating arrangement, the 4 masks it contains would all drop), but the masks in Boeing airplanes at least are electrically activated, so physical damage to the cabin ceiling seems unlikely to cause a mass deployment.

Now, if the cork happened to hit the switch in the COCKPIT, then perhaps all the masks could deploy then.  Normally the masks drop only when the system senses a cabin altitude in the range of 15,000' MSL, but there is a switch the pilot can use to drop the masks if you get the rapid depressurization up high and the automatic system failed.  Typically this switch is safety wired shut for obvious reasons, but if some operator didn't use safety wire and the cork hit the switch JUST RIGHT, then this scenario might work.  (We're talking a one-in-a-million shot here, but it might be possible.)

There are stories of hard landing sometimes dropping one or a few rows of masks -- this happens when the latch on the container isn't quite as secure as it is supposed to be, and as long as nobody reaches up &amp; activates the flow of O2, it's a pretty simple maintenance procedure to repack and restow the masks.  (If somebody DOES pull down &amp; activate the O2, then the oxygen generator canister for that unit has to be replaced, and that's a more lengthy process -- especially if the generator isn't on hand at that airport!)  So a physical shock from a flying champagne cork being enough to drop the masks from ONE unit isn't too far fetched, but unless you're talking about a really old design where the signal to all units went out mechanically instead of electrically, I have a hard time believing this scenario. (Please note, I'm not claiming that even in the oldest designs a mechanical linkage connecting all the units would necessarily be present -- just that modern designs are NOT mechanical until you get to the latch on an individual unit.)

And noting that the plane isn't allowed to fly with masks hanging sounds right... but 7 hours just for repacking one unit seems rather lengthy.  I'd suspect that the paper took the facts of ONE unit deploying, and artfully crafted it to sound like lots or all of the masks dropped.  Sensational writing?