I think it would help to understand that your insurance company didn't actually change networks - what changed is that your doctor is no longer a member of the insurer's network. That can happen for a lot of reasons - sometimes the doctor just doesn't want to accept the fee/reimbursement requirements of an insurer, and sometimes a doctor no longer has admitting privileges at the hospitals in the group. For example, we have a health insurance plan in New England started by a number of the big Boston hospitals (Mass General, Brigham & Women's Hospital, and so on). If an individual practitioner is no longer associated with any of those hospitals, he/she is no longer in the network because there's no place to send his patients. And if a doctor (r physical therapist or psychiatrist or whatever) no longer wants to limit his/her fees to those allowed by the insurance company, they can't stay in the network.
An example you may be familiar with is when you have a car accident, and the insurance company gives you a choice of certain body shops you can use. You can choose freely among those, but if you go to someone else not in that "network", your coverage doesn't apply. These body shops have agreed to charge certain prices for certain work, and not go above that price limit. In exchange, the insurance company says, "We'll put you on our list for all our policy holders, and if they need the services you provide, they can choose you. You'll get guaranteed customers by charging only a pre-approved price for each type of repair."
Ostensibly, these networks keep your costs down. You aren't paying extra for this.
So the insurance company isn't actually paying a network - it's not like there's a master network like an internet service provider! The network is just all the practices that are members. You are in the network - the doctor's office no longer is.
Because these changes in medical coverage happen all the time, the insurer can't possibly notify every single policy holder who might be a patient or have been a patient of that practitioner at some point in the past. That would be logistically and financially impossible. They publish a printed list probably twice a year, and you can check on line for a list of participating "in network" providers. When you booked your appointment, the receptionist should have asked you what insurance coverage/plan you had, and should have let you know that they were not longer accepting it. It's the doctor who is motivated to get paid, either by the insurer or the patient. In my view, it was the job of the practice to verify your appointment when you made it. If you made it six months before the practice dropped out of the network, then the office should have written a letter to everyone in their file who also had an appointment booked to say, essentially, "According to our records, you are insured by XYZ insurer. Please be advised that we no longer accept this insurance and are not part of XYZ's network. Therefore, if you wish to stay with our practice, you will be responsible for all costs. If you have changed insurance coverage/companies, please contact our office to verify that we accept your new policy." So they fell down on the job and didn't tell you until you arrived, which was a bit unfair and very inconvenient.