Apple deals with the rumour sites just fine as it is. Considering the volume of stuff out there very few web sites get the attention of Apple legal, and infrequently. You may be correct that rumors on rumor sites cause Apple little or no harm and may even benefit Apple but at times the rumors gain more momentum, they get picked up by regular news outlets which can cause real harm for Apple.
You may have noticed it is somewhat cyclical and recently the cycle has been on the up, more rumor stories have appeared in regular media citing rumor sites as sources. Apple has to smack down the sources first (companies have an obligation to protect trade secrets, copyrights etc otherwise they lose the ability to protect their 'property') which sends a message to the republishers. These guys then also stand the chance of being sued and actually have resources that could pay Apple's claims should they win. The regular media types also have lawyers in house who will advise against publishing infringing articles when Apple is clearly on the case.
This particular unannounced product is even more worthy of protection than most Apple innovations because it is an entirely new product category for Apple, music creation hardware. It's not just the usual smaller, faster, longer lasting battery innovation, it's a new product in a new category and the competitors include small, nimble manufacturers who can get things to market faster than Apple. Also bear in mind that music has more fans than computers and plenty of them are fanatics.
Your suggestion that Apple feed false information to rumor sites is crazy. Under some circumstances it would be illegal (eg SEC regulations) and it would piss off the 'Mac web' but most of all it is inconsistent with Apple's ethical approach to life. Knock a Mac rumor site off the net and another will spring up in it's place, there's always three or four, the names and personalities change.
Apple legal tend to smack down a couple of rumor stories per annum and it seems to be only when they are truly concerned that the rumors are harmful. I'd say Apple has got the balance just about right.
"The reasons Apple has for an extreme dislike of rumors are easily guessed (and guessing is the only option available)", is a great example of how a short sentence can be totally incorrect in three ways.
1. Apple does not have an extreme dislike of rumors.
2. The reasons there for are not easily guessed.
3. Guessing is not the only option available
Rumors: One More Good Thing for Apple