It's not just the TV set, it's anything capable of receiving TV broadcasts. So a satellite dish plugged into a laptop would count, but a TV that isn't plugged into any aerial wouldn't count.
The opt-outs you're talking about Peck aren't, in practice, particularly useful. The TV license goons are so thick-headed that they just assume that every household has a TV, and that every TV needs a license. Borachio's post about the menacing letters insisting that he had a TV and that he would have to pay are entirely reflective of my experience too.
Additionally, the divorce you're talking about between paying for a TV broadcast and paying for the actual content is part of what I meant when I said that it probably made sense 60 years ago, but doesn't make sense any longer. It made sense to pay a license per TV set back in the 1950s, because at that time, (a) a TV was necessary to watch BBC content on, (b) if you had a TV, then you didn't really have a choice over what to watch -- you definitely were watching BBC content at some point, and (c) only rich people could afford it anyway, meaning that it didn't matter that the whole thing was a regressive tax. Now, though, none of those things are true, and the license fee makes little sense.
I really can't see any rational, reasonable argument for keeping the license fee. Arakhor's argument is simply FUD. I mean, why don't we just pay for everything with a flat license fee? Let's have a flat hospital fee instead of paying for the NHS through taxes, or a flat school fee instead of paying for education through taxes, or a court fee instead of paying for courts through taxes, or a fire fee instead of paying for a fire department through taxes. I would love to go on, but you get the idea. It's a nonsensical way of paying for a public service. The fact that there is still a specific fee for Black and White TVs just shows how antiquated the whole system is. Modernise it, rationalise it, make it fair and progressive.