Re: Not free, just not expensive.
"Except in this case the user is paying for it to be produced in the first place."
No. The License Fee covers a small proportion of the BBC's expenses and—here's the crucial bit everyone seems to have missed—the BBC are REQUIRED to use external production houses for a set proportion of their output. (I forget what the exact percentage is, but it's somewhere in the range of 40-60% bracket, I think.)
"Spooks" is therefore NOT "owned" by the BBC. They merely paid to license it. The BBC may have fronted up some, most, or even all, of the up-front costs—for which they got the rights to have first dibs on broadcasting the show. The BBC might even have finagled a distribution contract deal through their BBC Worldwide arm too, so they get a bit more money out of it.
But remember that for every success like "Spooks", there's at least one utter failure like "Bonekickers" which disappears without a trace after a single season. And usually rather more than one. The BBC needs to balance the books, so every hit ends up paying for a bunch of misses.
The BBC's former Director General, John Birt, is also responsible for the second greatest f*ck-up in privatisation history, (second only to the privatisation of British Rail). He literally forced every single department—every producer, every studio, etc.—to "compete" with each other for work! This farce is named "Producer Choice" and means every show's producer must choose whether to make a show in-house, or farm it out to a third-party service provider. As a result of Birt's blinkered stupidity, a shitload of BBC employees suddenly found themselves working as freelancers and consultants... for a hell of a lot more money than they'd have made if they'd stayed in-house. John Birt is truly the heir to the throne to the Kingdom of Idiot.
The upshot of all this is that, no, the BBC often does not "own" much of what the public think it does. Look at the closing credits of "Red Dwarf" and you'll see that the later series were produced by "Grant Naylor Productions". Every single episode of "Have I Got News For You" was made by "Hat Trick", and so on. (Ironically, there are even programmes in the BBC's archives produced by the remnants of Thames Television!) And the same is true for a lot of radio productions too now.
Take a good close look at the end titles of a lot of BBC programming and you'll be surprised at just how many hit shows are actually made outside of the BBC.
The BBC are also well aware that they may not be able to rely on the TV License fee for much longer. (Never mind that the same fee is also paying for the rollout of rural broadband and a bunch of other projects; the BBC doesn't get all of it anyway.)