I don't see how they can guarantee that unless they can maintain completely separate backhaul paths from wherever the linear channel bandwidth is measured and controlled (cabinet/exchange/wherever). To take it to an extreme, if all or most Infinity users connected to a cabinet or exchange were to be watching one HD linear channel and recording another at the same time (hypothetically the World Cup final/Champions League final etc.) there would be an obvious risk that they'd have to take a big chunk of bandwidth from all ordinary Internet users in the area, to maintain linear channel quality, and that it would make a big dent in everyone's Internet speeds at the time.
I'm sure they will plan for this possibility and I just hope they get it right, I've got well used to my 75Mbps rock-solid 24/7 internet speeds now and I quite like it!
BT is able to do this, they sell a service that any ISP can buy that gives them guaranteed bandwidth for a set period of time. It was available on ADSL, I don't know if it has made the jump to fibre. They have used it for BT Vision customers while downloading VoD.
The fibre services have a pretty hefty guaranteed throughput - I think it's 12 or 16Mbps, so it's up to BT to build a network that can meet that + any other demand from other services. At least the cabinets should all have spare fibre for more backhaul.