You really aren't missing anything here at all as it can become extremely complex if you don't have a witness who can put you at a certain place at a certain time which is anywhere other than the crime scene and be corroborated by either an additional witness and/or digital evidence.
But the notion that you either have an alibi or you don't isn't correct until either can be proven as fact.
An example of an alibi without a witness could be as follows.
The defendant has been charged with a crime allegedly committed on King Road, Moscow, Idaho between 4:00 AM and 4:25 AM.
The defendant claims to have been running at the Arboretum and Botanical Garden, Moscow, Idaho at the time of the alleged offense which is roughly 1 mile from the scene of the crime, but since the defendant was alone during his run, there are no witnesses to corroborate their alibi, so the defendant must use other means of evidence to support their claim.
Digital Evidence: If the defendant uses a fitness tracking app on his smartphone or smartwatch, it might have recorded their run. This data could provide a timestamped route that proves they were at the Arboretum and Botanical Garden during the time of the alleged offense.
Surveillance Footage: The Arboretum and Botanical Garden or surrounding areas might have surveillance cameras that recorded the defendant during their run.
Physical Evidence: If the defendant made a purchase at or near the Arboretum and Botanical Garden before, during, or after their run, a receipt could serve as evidence.
As you can see, there are multiple examples of an alibi, the biggest problem would be the defendant convincing a jury about said alibi.
As i stated above, an alibi without a corroborating witness can become quite complex.
And this complexity can potentially result in a judge granting an exception to the defendant for any of the requirements of
Notice of defense of alibi