This is one of the reasons why it's always a good idea to put all of your complaints in writing, and save a copy for yourself.
Ask the LL, in writing, for a copy of the plumbers bill, with an explanation of how they determined you must have been tampering with the toilet, and a list of what repairs they made.
A lot of landlords in the city replaced toilets several years ago when the city offered rebates for water saving models. I don't know if they're required by city law but it certainly indicates you had an old toilet.