The tenant should report water leaking to you as soon as possible. If it is apparent that the water is leaking, then the tenant should take all steps to try to turn off the water and call the landlord or landlord's representative as soon as practicable.
Your problem is that it would be very difficult to prove when the leak started and how bad the leak was.
It is possible that the water leaked onto the floor while the tenant wasn't there, it got wet and the tenant did what he could to mop it up.
I hope you have insurance to take care of this, because this is normally a landlord problem.
If you think you can prove it, have the plumber give you his professional opinion as to how the leak happened, how bad it was, and whether or not he can pinpoint that the tenant could have prevented any of the damages that you claim.
If you haven't returned the security deposit yet, you can fix the floors and claim he was responsible and see whether or not he objects and/or wants to sue you and maybe win up to 3x damages if he can prove you withheld his deposit in bad faith.
You can continue to discuss this with your ex-tenant or sue for damages if you already gave back the deposit or see if he sues you if you didn't. I hope it isn't that bad, but I do know hardwood floors do cost a lot to repair. I hope you can cut out a small section and get it done.
This is general legal advice intended for informational purposes only and does not create and attorney/client relationship. If you wish further advice, please contact an attorney of your own choosing or you may contact me for further advice and make other arrangements including retaining my services.
You could try to hold the tenant responsible, but you would have a difficult time proving that the tenant knew about the leak, when it started, that the tenant did not clean up any leak, or that they did not promptly report it.