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I haven't used webstats so I don't know the answer for sure. Looking at their demo, I couldn't see any evidence that it tracked spiders. My guess is that they exclude them from the stats because they are not 'real' visitors. Most of the free stats programs are not set up to track spidering activity at all.
with your situation, I would just detect the HTTP-USER-AGENT on the pages and send an e-mail or run some script for notification if GoogleBot comes.
I don't think google is against this. But please verify at asking around. I won't pay a buck to any stats s/w for this one simple problem.
Let me know if this helps.