It can't be true, because sometimes an item drops twice in a row.
Whenever you kill a mob, it has X% chance of dropping items, no matter how many mobs you killed before, how many mobs were killed by other players, how long it respawned, how many mobs currently respawned, what your level is, what day of the week it is or what emote you used prior to killing it. So basically, if you're farming a rare drop, it has the same chance to drop in the next 5 minutes, whether you just started or are already farming there for 6 hours straight without luck.
SynnTastic> The server that felt empty to you is probably an endgame server. Most people there already hit 60, possibly a long time ago, and are just enjoying the lvl 60 instances, the raid instances and the bg's. Going with a new server sounds like a better choice to me, and even though Hogger got farmed to death, don't let that withstand you. That'll get less problematic fast as people get a little higher. Keep in mind that leveling 1-10 and 10-20 are stuff you do in a single evening, so the availability of the mobs keep in mind everyone streams through pretty quickly.
Also, keep in mind that most of the better stuff is in an instance. In an instance, no matter how many people are running that instance, your group gets your own copy, with your own mobs and your own drops, unaffected by anyone outside the party.
Really, as long as you don't suffer from queues, I'd say, the more the merrier. It's an MMO after all. And more people will make it a lot easier for you to find a party for a specific instance.