The rumor table is a time-honored tradition in adventures. They can serve as springboards to the parties adventures, providing clues on where to get started, alternate theories and locations, local color, and a host of other events to drive the play forward, be it on the correct tract or an alternative one.
Rumors should be specific and "in voice" when possible. Bad rumors are presented in an abstracted form. "Goblins are raiding the farmsteads." Good rumors offer a degree of interactivity. Two farmers, talking to each other at the feed lot, trying to decide if they should move because of the goblin raids, or how to better protect themselves, or how ol Jed and his family and were raided and his oldest, Nick, was killed. These present opportunities for interaction, a roleplaying element where the party gets to interact with the farmers and bond with them or pump them for more information. Notice the specificity. It's not a farmer and his son. It's ol Jed and his boy Nick. These people have an intimate relationship with each other. That specificity reveals a lived in world, one that feels more visceral to the party as they interact with it. The designer, by providing that specificity, helps the DM to ground the adventure and build off of the seed planted.
The purpose of the rumors is to drive the adventure forward. It's how the designer helps point the party toward interactivity. They could be truthful or they could be false, but they should lead to something, some sort of interactivity at some point that is at least secondarily related to the adventure. Even in the case of false rumors, there should be something present; meeting someone or some other clue to help put the party on the right path, for example. Or even, as with the famous "Bree Yark!" provide some anticipated delight during the actual adventure.
You always focus on the forms of rumors, but I am much more interested in their content. I feel like a rumor should always have a function in addition to driving conversation with NPCs. Off the top of my head, I would say that rumors should do something like: provide a hook; provide a clue, or tell the players something about how the (fantasy) world works.
I also feel like even false rumors should move players closer to the truth. For example, a false rumor that is a hook should still pull the players into an adventure, just possibly a different adventure than they expected; and a false rumor that is a clue should still move the players toward the next clue, even if the original clue suggests a wrong conclusion.
I'd add that a rumor table doesn't always have to be at the beginning of the adventure. A prisoner might know more rumors, or a village in the wilderness may have a bunch of their own rumors. This can provide little side quests or situations so the adventure or main goal isn't linear. Exploring and discovering something in a dungeon can be fun....but learning about something while in the thick of a dungeon and then discovering it (and knowing what to do) doesn't only fit the exploration/discovery node, but also the 'reward' node.