Obviously, but that misses the point. Virgin have their own network to provide service for their customers. You are not, so far as I can tell, connected to Virgin, you are, I assume, connected to Openreach. There are interconnects between the different networks to allow calls to move between the different networks. Virgin are no more dependent on Openreach to deliver a call from one of their customers to your phone than Vodafone are dependent on O2 when someone with a Vodafone mobile phone calls someone who has an O2 mobile phone.
Just to be clear about this, when you have a Virgin cable connection, you get two cables to your house: a coax for the digital stuff, and a twisted pair for analogue telephony. Virgin have their own exchanges to service the analogue telephones, which obviously interconnect with BT's network and all the rest. You can choose whether you want telephony via your Virgin connection or not.
Virgin don't ring your phone, your service provider does that. Virgin pass calls for you over the interconnect to your service provider and leave the rest up to them.
BT don't have a network, you are thinking of Openreach. BT just sell services delivered by Openreach.
The rest of what you say looks good to me.
Technically, yes, but: "Openreach Limited being wholly owned by BT Group plc" - Wikipedia.
They do if Virgin is your service provider, as it was for me.
Well, that's such a relief.
Yes, but BT Group PLC are not the company that sell telephony to customers, they are another subsidiary.
In this case 'your phone' meant Mike's phone as I was replying to him. I didn't mean anyone's phone, just his.
Well speaking for here in Australia, which I am sure would be the same elsewhere, the ATA is part of the VDSL or fibre modem which you get when you are "switched over" to "broadband".
You have essentially three choices. Use the VDSL only for the "old" analog phone if like my mother-in-law, you believe the Internet and mobile phones too much to understand; use the analog phone and broadband internet; or as many people do, use only the Internet and have a mobile phone as a "phone".
I've seen 'free' routers with analogue telephone ports, so maybe that's how it will be provided to the general public. I don't use a free router, I have a decent Draytek router (and an OfficeServ 7100).
Fibre modems present an Ethernet connection for you to connect your own router in the UK. I imagine that before long there will be fibre modems with built in routers and analogue ports. I don't want the free stuff, it's always poor quality.
Well - politics here - the Gov (when it changed hands) decided we couldn't afford FOTP so we got FOTN and little green boxes started springing up in the streets. We were forcibly changed over and when we got the new contract with whoever, we got our VDSL box with one or two ATAs.
We were offered to pay $500 if we wanted not to actually get FOTP, but to learn whether we could get FOTP and how much it would cost to get it. I gave up at that point. 
Obviously (or mind you ...) new development areas will only ever have FOTP.
Paul, FOTP and FOTN are different to the terms we us in the UK. I am guessing FOTP is fibre to the premises and FOTN is to the street cabinet with final delivery over copper, is that correct?
Yes that is exactly the point I was making.
I can see the little green box from my house. It has fibre to it. Serval times a day men come to kneel by it, so it must be some sort of shrine where they worship the new god.
My ISP is not BT or Openreach but they do rent that last bit of the line. The point I was making was that even Virgin have to do that and no matter what happens to the UK service they will have to continue to do that.
I am in a rural location and there is no way Virgin are going to dig up the road where I live.
I'm not sure Mike if we are violently agreeing or if there is some point I should still clarify. Anyway, unless someone has a clear question I'm going to end this part of the discussion here.