I am skeptical that you could buy shares after expiration and say that those are the shares that you delivered instead of the shares that you had owned.

You might be skeptical, but it can be easily done, and it is easily done all the time. I've done it myself a few times over the years. Not only have I done it for "normal" Saturday expirations and assignment over the weekend, but at least once I did it when someone swiped a dividend from me on the top half of a bull call spread that was on a weekday, not on a Saturday. I jut looked it up, they were Apple 500 strike calls, exercised and assigned to me on Wednesday 8/6/2014 after the close. On Thursday 8/7/14 I purchased a bunch of shares to deliver, and delivered them. To add insult to injury, I also had to pay them the dividend (that's obviously how it works because they exercised and bought it at ex-div and I delivered after ex-div, that's how you "swipe" the dividend) of $0.47! But to make up for it, at the next ex-div day, on 11/5/14, I exercised the bottom half of that BCS, the 400 strike, and captured the dividend from whomever wrote those 400 strike options and was assigned with my exercise. And, sure enough, on 11/13/14 they paid me a $0.47 dividend!

One way to think about it is with the following thought experiment -

1. You sell (to open) a $100 strike call in stock XYZ.
2. Some time later, it expires on Saturday in the money.
3. Over the weekend, your broker notifies you that you have been assigned.
4. Come Monday morning, what do you do? You have to buy shares of XYZ to deliver (because you have no XYZ shares in that account).
5. Voila, you've delivered shares that you purchased on the Monday following the Saturday of assignment.

Do the same thought experiment but with owning shares of XYZ in another account.
Do it again with owning shares of XYZ in your own name (formerly "paper stock certificates").
Do it again with owning shares of XYZ in this account.
Do it again with owning MANY shares of XYZ in this account all at a different basis.

The whole system would be terribly unwieldy if you couldn't choose exactly which shares to deliver.