No matter what is said, there are two distinct phases to fermentation.
1) Aerobic phase:
Oxygen is required for healthy yeast. This phase lasts until the SG is about 1.010 to 1.020. If you get the rotten egg smell during this first phase, it is likely because the yeast are either starved for oxygen or they need a nutrient. Most (but not all) wine kits do not require a nutrient to be added.
2) Anaerobic phase:
Oxygen should be kept away from the wine, as the yeast no longer need oxygen and the wine surely doesn't need it, either. This phase starts at about SG 1.010 to 1.020, right after the previous stage.
Some kit instructions say to seal the wine during both phases. This is more because they are concerned the wine will get oxidized, since a wine, such as a weak mist kit, can survive the aerobic phase sealed. (Better to starve the yeast than have oxidation, I guess.) This, however, is not the best for your wine. Learn to protect your wine from oxygen without having to starve your yeast of oxygen during that first phase.
During the first stage, very little oxygen can get to the wine, anyway. The CO2 is bubbling out very strongly and is heavier than oxygen, so it protects the wine by pushing out almost all the oxygen. During the second stage there is much less CO2 to displace the oxygen. Hence, you seal the carboy with an air lock that lets out the excess CO2 and won't let air in.
Kits with grape packs can usually survive being sealed during the first phase, because you have to open the lid at least twice a day to push down the grape pack cap. This generally lets in enough oxygen to "get by".
If you want a good fermentation, don't seal the lid down during aerobic fermentation. put the lid on in such a way as to keep flies out. Place a cloth over the air lock's hole and maybe even place a towel over the top of the lid to protect it.