I had that happen to me too. I booked a very expensive (relatively I guess) reservation at a hotel, something like 7 rooms for a decent period of time, for a group of co-workers, and got a HH Silver card in the mail soon after.

Granted I don't know if those two things are related, but that's the only trigger I can think of. Odd as I hadn't even stayed there yet. Later we did in fact complete the stay, and paid for all the rooms with one CC charge. And I went on a mini-run of Hilton stays, just a couple more in a few week period, all airport locations. Then I got a HH Gold card in the mail a couple weeks later.

Once again, I have no idea if A led to B with this, but given I had no other obvious interaction with Hilton -- I didn't have a HH Amex (though I do now) and I was AA PLT but had been so for a few years -- that's the only theory I can come up with.

If I had to make a wildly speculative guess I'd say there's a computer or even an office that notices things, in my case an out of nowhere drastic increase in spend and stays over a short period, and decides to capitalize on it. One reason I suspect this, is that it actually worked quite well. I was very much loyal to SPG (as a gold there) but found that HH Gold was much better, at least in my experience. So now I stay SPG only when it's clearly more convenient (still gold and will stay there due to SPG Amex spend) and try to steer my stays to Hilton when I can as they treat me very well. And with AA >> HH points transfers being simple and very quick I can almost always top off the account quickly (from my wife's account) if I need to do an award stay. Quick enough even that I managed to check in, decide I liked the hotel enough to stay longer, transferred points the same day, and by day 3 they had gone through and I could add another couple nights.

But that last part is going off topic. To echo your observation I also had a "no idea why" experience too, my theories aside. It seems that HH might have some sort of proactive program for these kinds of things.