[drewcrawford]

The term is based on a figurative bug being found. OED traces this usage to

> Mr. Edison, I was informed, had been up the two previous nights discovering ‘a bug’ in his phonograph—an expression for solving a difficulty, and implying that some imaginary insect has secreted itself inside and is causing all the trouble. - The Pall Mall gazette, 1899

which seems to be reporting a bit of jargon in use at Menlo Park at that time that would be completely unfamiliar to the reader.

At some point the jargon spread more widely in engineering culture, this usage from The Journal of the Royal Aeronautical Society 1935 assumes some familiarity with the term, and attributes it to a whole country instead of a lab:

> Casting, forging and riveting are processes hundreds of years old, and, to use an Americanism, ‘have the bugs ironed out of them’.

In this context, the "First case of an actual bug being found" would be the first time that a problem was traced to a literal bug, instead of a figurative one. This would have been engineering humor, as if Google Cloud Platform went down due to a thunderstorm.

As the term "bug" became more closely tied to computer culture, we started thinking of its origins in strictly computer terms (and so you pose the question about the invention of the "computer bug"). The moth story is certainly an early usage in computing, and was a major inflection point for the computing usage, so as origin stories go it is a reasonable answer to the question.

It's just that the label of the computer bug does not reflect the real development of the term. Bugs were part of the engineering jargon long before computers, so the extension of this vocabulary to yet another engineering field would not have been notable at the time.