...that's not as silly as it might sound.
Rupert Murdoch sold out his US satellite interests to US "cable" king John Malone last year. Murdoch has spent decades trying to build a global satellite venture and when he eventually succeeded, soon after he sold the US Dish Network to Malone. Although the only reason given was that Murdoch didn't want Malone to get a controlling interest in his parent News Corp company. There was, I think, another reason too.
There have been various articles over the years that Murdoch's kids, especially James, have told Daddy that the internet is the future. Which I agree with. Satellite TV will always be (with current technology) primarily a one way medium. Rupert Mudoch has seen how the internet has eaten into his various ventures, ie people look at newspapers on the net, rather than buying them from shops.
Rupert Murdoch likes to control everything. A reason why he set up Sky using encryption technology from one of his other companies and moved all his channels to "his" own satellites. Eventually, Murdoch was told that Sky had to be an open platform. As long as a broadcaster has the money to pay Sky's EPG fees, anyone can broadcast on Sky. So, we have the situation today where there are now 100s of shopping, ethnic, quiz, god, dating and other rubbish channels on Sky. Not what Murdoch wanted. Virgin Media, on the other had, is a private network and clearly doesn't want all of these rubbish channels on its service. They recently got rid of all the quiz channels as an example of this.
I would not be surprised if Rupert Mudoch and family, at some point, don't get involved in cable and the telecoms industry. Perhaps a bid for AT&T at some point? As for Virgin Media, it's in so much debt that if Murdoch did go to all the other main VM shareholders (other than Branson) with a proposal. I think they'd be interested. If Murdoch doesn't adapt, he'll be left with an old fashioned, one way satellite business when most people in the near future will be "viewing" tv/films via the internet......
As for Richard Branson, HE is Virgin. HE is the brand. No matter what people think of Sky (I think they're great) it's a powerful brand. Now cable has one too, but is it too late...?
Isn't it curious that Branson launched his biggest Virgin company this week and he's on telly constantly talking about stem cells and saving the climate too. What a coincidence
Finally, onto the OP's question....
Branson is the largest shareholder in Virgin Media and the company is using Branson's brand, which is himself!! This combination, I think, gives Branson a material influence over Virgin Media. Although he doesn't run day-to-day affairs, I believe he now makes the big deccisions in the company. Thus, it's Branson who is running Virgin Media. A bit like the ITV situation with Murdoch...