I imagine there are a fair few reasons for this, from HSE regulations to them not having insurance in case they fall through your ceiling, all of which are acceptable reasons not to run it in your loft.
However, the main fault here being they shouldn't have told you on the phone that they would do it, then when your engineer shows he isn't allowed to do so.
Your only real option is to allow them to run it round the side of your house if that is possible.
Guess that option is out, hence why you are in this situation.
There might have been in the past but regulations and such change. I believe Sky installers are in a similar position too from the last few I spoke to.
You could try running the cable in yourself, but I'm not sure if the VM engineer would be happy to use this or not. Another option I guess would be to have it from downstairs (guessing this is where your incoming connection is) up and the under the floorboards to your bedroom at the back. Again, you would probably need to lift this and make sure the route is clear so the engineer can just lay the cable down essentially, but again couldn't guarantee the engineer would be happy with this.
Not sure this is fully accurate, I have 2x V6 boxes connected via Ethernet, I just unplugged the coax cable from one of them and it lost signal, so it's not like the coax signals from the other one are sent over Ethernet instead.
Unless you do have this working, I would be interested to know about the possibility, but as far as I know all VM kit (router, V6, TiVo) have to be connected to coax, which the OP is having issues getting installed.
Can you drill some holes in your ceiling and floorboards and have a pull rope to draw the coaxial and Ethernet cables through the loft and into the bedroom. The VM technician can then do the connections and testing of the signals.