Can anything cause the battery "cycles count" to appear higher than it really is?
A faulty sensor could do it. Apple says:

"A charge cycle means using all of the battery’s power, but that doesn’t necessarily mean a single charge. For instance, you could use your notebook for an hour or more one day, using half its power, and then recharge it fully. If you did the same thing the next day, it would count as one charge cycle, not two, so it may take several days to complete a cycle."

Looks like a good case for a visit to the Genius Bar, and perhaps having your battery replaced. I agree it does not seem at all plausible that your cycle count is higher than the days you have owned it.