Sorry, that's definitely not the problem. All the VAFC could do is tell the car to kick into vtec and modify the map sensor signal.

Even if the VAFC did cause the the rocker arms to be locked into the vtec position (i.e., you tried to start the car with VTEC engaged), the rocker arms only lock so that they all follow the larger camshaft lobe. There is physically no way that the VAFC caused your rockers to lock and the cam to stop spinning with the timing belt. Even with VTEC engaged, the cams will still spin with the timing belt... if they didn't, you'd be skipping teeth everytime vtec engages while you're driving.

If your cam skipped teeth, there's onlyone reason it could've happened. The tension on the timing belt was not enough to cause the cam to spin with the belt.

This could be due to: 1) the camshaft was providing too much resistance, so that it was easier for the timing belt to skip teeth over it instead of turn it (i.e. it was easier to skip a tooth than to spin the cam).
2) The timing belt was not tight enough. so that it was easier for the teeth in the belt to lift up and over the cam gear instead of spinning it with the motor.

I'm betting its #2. Your timing belt was probably loose. Did you work with it (or have any work done to it) recently? If so, its possible that whoever worked with it last did not tension it properly, which could definitely cause this problem. Perhaps your tensioner is going bad: If the timing belt was tensioned with the right procedure, but the tensioner was bad, it can cause the tension to still be less than optimal.