Since the post doesn't mention anything like "we reviewed logs and confirm the key was not accessed", it is very likely that they either don't have logs that are reliable enough to rule it out (e.g. they may be sampled or otherwise incomplete), or that the key was accessed.

Keeping a complete log of all GET requests to random files in a public repository in a reliable way would be insane.

No, it wouldn’t be - assuming by “insane” you mean “silly to do”. I build systems at Google that do exactly that.

Whether it’s worth the cost is a decision each company makes. Also, you don’t need to keep the log forever. Max of a few weeks retention would be common.

Presumably, keeping 'last remotely accessed' and 'last remotely modified' for every file (or other stats that are a digest of the logs) is sane for pretty much any system too. Having a handle on how much space one is dedicating to files that are never viewed and or never updated seems like something web companies that have public file access would all want?

What guarantees do these systems provide? Are 100% of requests where data was served guaranteed to either end up in the log or at least create a detectable "logs may have been lost here" event?

Or does it log all the requests all the time as long as everything goes well, but if the wrong server crashes at the wrong time, a couple hundred requests may get lost because in the end who cares?

It's not just GET requests. Someone could have cloned/refreshed the repo using ssh. The repo might have been indexed by github's internal search daemon which might not use the public HTTP API but uses internal access ways however those might look like. You might have purged the database of that daemon but what about backups of it? What about people who have subscribed to public events happening in the github.com/github org via the API?

You'd have to have logging set up for all of these services and it would have to work over your entire CDN... and what if a CDN node crashed before it was able to submit the log entry to the log collector? You'll never know.

One H4X0R gave it to four friends, who in turn gave it to between 9 and 14 friends, who in turn gave it to between one and 6 friends.

If train A leaves New York going 60 miles per hour with 167 people on board and train B leaves Chicago one hour later with 361 people on board going 85 miles per hour, how many people now have the key?

The answer is 31337.