Huh, you know, that sounds just like how dimensional analysis affects people sometimes. I've certainly seen some take a pile of engineering inputs and whack them together until the units work (myself included); it's a shockingly powerful heuristic for linear systems, since you'll typically only be off by some logical scaling factor. Of course, there's a bajillion ways it can deceive, so it's wise to be thorough.
It has to do with how abstract and parametric the code was. There may very well be only one valid type-checking program which exists (so long as you do a cursory check against infinite loops and error throwing).
So, it's a gamble---do there exist any other non-trivial programs at this type?
If not, then I know my code written is correct without testing.
If there are, then I'm risking that I found the right one.
This is why Haskellers get so excited about "parametricity". It's the core tool that exacts this property of "there are only a small number of programs which could ever exist at this type" which drives correctness.
"...I actually had no idea how the function worked. I simply wrote a function that matched the required type."
I guess everybody have done that. But releasing it without testing... I'm just impressed, in both a good and a bad way.