The blockchain has timestamps, so actually you can verify quite easily. Unless, for some reason, the individual is sending bitcoins to himself...

That is the implication. He got sent very large sums of Bitcoin, you would expect that he'd just get a bunch of small ones, but he got 2-3 large ones ($5,000 a piece).

Maybe from people who didn't realise how much they are worth?

What number of people do you think qualify:

1) Have 5+ BTC 2) Recognize a QR code on a TV broadcast 3) Think to pause the tv broadcast, decode the QR code and send BTC 4) Completely unaware of the 1000s of news articles and broadcasts about the soaring value of BTC

Maybe he sent it to himself, maybe someone else was just very generous, but no one purposefully sent 5BTC without knowing it was valuable.

Or perhaps they do and have quite a large number of them.

What exactly would be the point of sending BTC to yourself?

More publicity for bitcoin, to drive the price higher.

He's donating 20 of the 22 BTC to Sean's Outpost so it's unlikely he would've done that with the sole intention of driving the price higher.