Who is at fault??

The question is more about WHY the toilet stopped working.  In my opinion I would just fix the toilet and keep my tenant happy.  A leaking toilet is usually a very simple fix and will cost you probably no more than $12 for new plumbing parts.
Most likely, the tenant didn’t cause the toilet to malfunction due to neglect or failure to maintain it.  Its just one of those things that happens and should probably be your responsibility as a landlord.
To avoid this problem in the future you should change your agreement.  If the wording leaves too many questions such as who is responsible etc,  it probably isn’t doing you much good to have it in the contract.  I’ve been doing this long enough to know that your tenant will say that it isn’t his fault, even if it was.    Instead, in your lease agreement you can have wording that says something like this:
——————————————————————–
Repairs and Responsibilities
Tenant is responsible for any and all repairs regardless of fault up to the amount of $50.  Any repairs above $50 will be the responsibility of the landlord unless the repair or damage was caused due to neglect or irresponsibility; then the amount shall be entirely the burden of the tenant.  Furthermore, tenant shall only use professionally state licensed individuals to preform said repairs.  
———————————————————————————-
I use something similar to the above paragraph.  It seems to prevent a lot of questions and repair problems.
I hope that helped.