I'm neither a lawyer nor a plumber but here is what I would do...
I would call a few locally licensed and bonded plumbers in the area, explaining the situation, and finding out what they would charge you to come out and inspect the problem - giving you a written assessment of what they believe the problem to be and an estimate (or, preferably, a bid) for what they would charge you to fix it (or finish fixing it). Based on the results of these calls (prices, general feeling about their responses, etc.), I would pay two or three of them to come out and give me the aforementioned assessments/estimates/bids - probably two at first and then, optionally, a third if the first two were significantly different. I would tell the property manager to hold up on the repairs until after you have the plumbers look at it. If they try to give you any grief over it, just tell them your insurance policy requires multiple, third-party estimates for a claim. Renter's insurance is generally very inexpensive until you have to make a claim, at which point your rates and/or your deductible typically rise very sharply.
If the plumbers' assessments differ from what the property manager stated then it will likely be well worth the cost of those visits. Assuming that is the case...
1) You will have two written statements from locally licensed and bonded plumbers (bonded meaning their insurance, not yours or the property manager's insurance, covers any future damages and required repairs due to poor workmanship during the original repair) stating exactly what they believe the problem was and what it would cost to fix it.
2) If the problem wasn't your fault, this gives you leverage against the property manager to place the responsibility for the damage and repairs onto them. This will potentially save you a lot of money, both upfront and in the long run, as the cost of those visits will likely be less than your deductible and your rates won't rise due to a claim on your renter's insurance.
3) If the problem was your fault, you'll at least know that you aren't getting taken advantage of by the property manager and you may still save money overall. You can also take one of those estimates to your insurance company to find out what affect that claim would likely have on your rates/policy, adding that to your deductible to find out your true total cost. At that point, there are a few ways in which you may be able to save yourself some money:
A) If this estimate is significantly less than the property manager's estimate then you may be able to get the property manager to reduce his estimate to match. At this point, if the cost is less than your total cost for making a claim, you're better off just paying for the repairs out of pocket. If not, then you've at least lowered the dollar amount of the claim which may reduce the amount your rates would rise.
B) If this estimate is significantly less than the property manager's estimate and he is unwilling to reduce his estimate, then inform him that you'll be using one of the third-party plumbers for the repairs and, if he tries to give you any grief over not using "their guy", remind him that because the plumber is bonded his insurance company can't complain about them doing the work - which is probably the number one bull-crap excuse for people trying to take advantage of you. And, as above, you'll know whether or not you'd be better off just paying for the repairs out of pocket.
C) If this estimate is the same as or higher than the property manager's estimate then you'll at least know that the property manager isn't taking advantage of you, whether or not the repair cost is less than your total cost for making a claim, and if you'd be better off just paying for the repairs out of pocket.
As I stated earlier, I am neither a plumber nor a lawyer and this is simply my opinion - and there may very well be some flaws in my logic. However, this is the approach I would take since - even if I end up costing myself a little more money overall due to the third-party plumber visits while still ending up making a claim - I'll at least know that I protected myself from being taken advantage of by the property manager.
Hope that helps!
