Robert, this sounds like a little messy situation. Apologies that you had this come up.
First of all I'd refer back to your lease. They most likely should have properly reported it to you if it was an emergency that way you can handle it, hire the proper personnel, & make the decision when you are advised of the situation. Them hiring it out themselves is on them in my opinion, because that probably goes against the lease on major repairs & how things will be conducted since it is your home & not theirs. Them being frustrated that the water isn't draining & they can't take a shower doesn't remove them of the responsibility of properly reporting it up to you so you can ensure the best course of action is taken..
For example in the lease I normally utilize in the Alterations & Additions section, Loss of Services, maintenance & repairs, & general provision - it goes over the proper reporting procedure as well as the guidelines for maintenance & repairs will take place. It also states that tenant must notify landlord of any discrepancies especially if it is an emergency. Granted there is more legal jargon & worded better in the lease, but this covers both parties in most situations.
Considering that the tenant had them come out without your consent & did the work, it sounds like it should be on the tenant. Now I am not an attorney, so don't take this as legal advice & I recommend seeking out an attorney in case if more stuff comes from this. Because with your decision to not pay the rest & put it on the tenant can stir up some commotion on both the company not getting their money & putting the bill back on the tenant. Not to say that this is how it'll go down, but there are certain boundaries that the tenant definitely crossed that can be a breach of contract as they did not have the legal authority to hire out the repair when it is your home...
And just because they may be inpatient, & that it happened potentially on a holiday weekend doesn't mean they have people do major repairs behind your back & expecting you to pay for everything. Because they could be saying that it is corroded, buttt that doesn't mean that it needs to be fully replaced in order to get it back In working order.
People can also say one thing without also providing proof of evidence that it actually needed to be done. With that being an extensive repair, I would be extremely upset that they went around to handle it on their own without the proper authority. I don't like being taken advantage of, and I don't trust companies that may say one thing is needed when it actually doesn't. (It's like when you take your car into a mechanic, & just because they can get an idea that you don't know anything they may try to sell you on replacing XYZ when they were all fine. This happens a lot with contractors & companies in order to keep a constant steady flow of work. Not saying this is prevalent, but you definitely have to protect yourself & trust those you hire to protect your hard earned wealth & assets). This is where you would have preferred to go with your preferred professional/contractor to get their opinion, then go from there if it is absolutely necessary.
Sorry for this being a long post.