It wasn't me this time
First off, with a gap that size she'd have been wrong not to try to get you off (much tighter could be a struggle, but not impossible).
The decission would have been made from experience in similar circumstances (what we're paid our peanuts for judging), and an assessment of the conditions and the operators and aircraft types involved.
Things that can go wrong:
1) Departing aircraft PAINFULLY slow to roll. If you can't accept an immediate (ie ROLLING!!!!!!!!!) departure, then don't accept such a clearance, wait for a better chance.
2) Controller misjudged the gap. If the inbound is a little faster than normal, she should have been able to tell (depends on her equipment), but sometimes it can catch you out. Also if its heavy then it wont slow down so much from four miles, which is difficult to know. If there is little or no headwind component on final, then things obviously happen a little quicker, but she should take all of these things in to account.
3) Controller or arriving pilot bottled out too soon, where it would have worked nicely given a bit of balls and an over the threshold clearance (or for lucky NATS controllers a conditional "after the departing ... cleared to land")
Of course, if she did get it wrong then it is logged as "pilot error" because it looks better on the records (much like your "ATC delays")
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I don't think its signifficant that there is an uphill slope to the runway. Each pilot she squeezed off in a tight gap would have to go up the same hill, so if 99% of the time it works, **** sometimes it doesn't and someone has to go arround.
Ramble over. Visit your local tower for a fuller picture!