I have a question for Shawn

Excellent follow-up question!

I am a little sleepy now, so I might revise my answer when I wake up fresh tomorrow, but here is my first attempt.

There is an important difference between your example sentences.

Quitting the band was the best thing that could have happened: As I said before, this means that there was more than one alternative past possibility, and quitting the band was the best when considered against all other hypothetical alternatives. 

For example, last year, I considered the following options:

-quit my day job

-quit the band

-move to a new apartment

-move to a different city

The only option that I actually did was to quit the band.  But now, when I consider all of the choices I had at that time, quitting the band was the best decision I could have made.

Quitting the band was the best thing that happened: This means that there was more than one thing that happened in the past, and quitting the band was the best when considered against all other past happenings.

For example, last year, I did the following things:

-quit my day job

-quit the band

-move to a new apartment

-move to a different city

I did all of those things, but the best of them was quitting the band.

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So, both expressions are natural but it depends on what you want to say.  Are you comparing and choosing among past possibilities, or are you selecting one past action among several others?  Please let me know if you have any other questions about this.