You can, but good luck. Filing a counternotice gets you the name (and I think the IP address) of the person that filed the notice, but considering that #1 is just a form input box and #2 is useless for identificiation purposes...
This was likely the act of someone with an axe to grind, not any violation of YouTube policies.
> We may then reinstate the material in question at our discretion.
So it's a toss-up if they're actually going to do something but they will reveal your information to the party that claimed infringement. That seems to be a pretty lousy deal.
It is an offense for a party to DMCA takedown content they do not own the rights to. This is assuming it was a DMCA takedown and not YouTube's internal system which doesn't have the same protections the DMCA provides.
Not that it makes it necessarily feasible, but at least there is an option.
This was likely the act of someone with an axe to grind, not any violation of YouTube policies.