Let me state a few things before getting into more detail:
1. Champagne and Burgundy are quite different wines and while there are certainly similarities, they are not the same and can't be treated as such. The issues that have affected Burgundy are both similar and different to some of the challenges Champagne has had
2. There is not a premox problem in Champagne although there have been issues with some wines maturing faster than normal in certain vintages. 1996 is one example and 2003 is another. While many have come to expect this from 2003, I'm not sure this had to be the case.
3. I'm an engineer who drinks too much Champagne and not a scientist so I apologize if I can't speak to the nth degree on anything. Sorry for the long and boring post below that wasn't checked by an editor so there are probably numerous typos.
1996 is an interesting case as it was a year like none other. High acidity, high potential alcohol, and high grape phenolics that went a little wacky in the Pinot Noir grapes. If you weren't careful in how you handled and pressed your Pinot Noir grapes, you could end up with a case where the phenolics tilted towards the wrong side and you were left with a wine that could mature/oxidize much quicker than expected even while maintaining a sizzling acidity. In a case where Champagne is a bit opposite than Burgundy, you really wanted to be gentle in your handling and pressing of Pinot Noir in 1996 in order to prevent too much phenolic impact in the juice. Adding to the situation was the case where some producers saw the wine going out of balance and decided to add Sulfur as soon as they saw things going unexpectedly. This did nothing but prolong the wine from going out of balance and rapidly maturing. It actually made things worse in a lot of cases as while a wine may mature early as a whole, it may do this quite unevenly between bottles (meaning some bottles will be well advanced while others not as bad). In this instance the same thing Burghound mentioned via corks and oxidation can be applicable to 1996 Champagnes that rely on a lot of Pinot Noir. By no means are all 1996s affected or all Pinot Noir heavy blends affected, but if you notice some of your Pinot Noir heavy bottles taking on some rather mature notes, this is why. Luckily for us all, I think Champagne learned a lot from 1996 and will know how to handle things better next time. A lot of folks in Champagne weren't ga-ga over 1996 as no one really knew what the wines were going to taste like when they were released. Some were spectacular, but it was the press that really drove this vintage. One other comment - once the affected wines start maturing early, they don't reverse their course.
Who had problems in 1996 - Bollinger, Billecart-Salmon, Egly-Ouriet, Lanson, Perrier-Jouet, and Veuve Clicquot are some who had problems. These problems didn't always mean a bad wine, just one that may have a blunted peak or may peak early.
2003 is an interesting case as this vintage was low in acid and high in potential alcohol. Everything you need for a tasty, open, and not long lived vintage. The juice in this vintage was very fragile with a lot of phenolics coming through that would cause the wine to oxidize and ferment very quickly. Most folks added a bunch of Sulfur very early on in the pressing process to prevent oxidation and attempt to preserve potential, but this didn't do anything, but prolong the inevitable and make the wine more unstable down the line. The potential for real greatness was never there in 2003 so attempting to hang onto this didn't make a lot of sense. If you made the choice to let the wine oxidize and stabilize itself before adding Sulfur later in the process, you may have given up on the false dream of greatness, but you got a better wine and one that likely will be longer lived. In addition to this, once the wines were in tank, Nitrogen could be used to force Oxygen out and create a reductive environment if desired.
The best example of who may have made a pretty darn good wine in 2003 by allowing the musts to oxidize was Moet/Dom Perignon. Time will tell, but I think they got things right in 2003 and the wines should be fairly long lived.
It is also interesting to look at exactly how different producers allow their musts/wines to oxidize. A lot more producers are coming to the conclusion that allowing a wine to oxidize a bit at some point can give it better balance and structure through its life. Whether this oxidation is very early on in the process or while the first fermentation matures, both reductive and oxidative styles can benefit from this. For oxidative styles, the classic way to do this has always been via barrel, but the concrete eggs are proving to be very interesting as they allow for some oxygenation without the impact of wood. Allowing musts to get some oxygen is also proving very interesting for those who prefer the reductive style.
It all comes down to balance and allowing the wine to reach its natural equilibrium. Forcing it one way or another may not always have a notable negative affect on the wine, but it can.