“Innocent until proven guilty” is an example of cargo-culting in personal ethics. Or if you prefer, following a process while forgetting the principle that drove the creation of the process in the first place.
The principle is that for most people accused of a crime by the state, the state has much, much more power than the accused. To act as one check against abuse of that power, we establish a higher bar for conviction of a crime than for innocence.
But if Frank’s lunch is missing from the fridge, and he thinks Homer ate it, there is no massive power imbalance, so Frank doesn’t have the same burden of proof to decide to dislike Homer, or to accuse Homer.
Of course, if the state listens to Frank and decides to charge Homer with theft, then the state has a higher burden of proof to impose criminal consequences.
If homer is declared innocent under law because the state couldn’t prove its case, we don't go back to Frank and harass him for making a false claim. His standard for accusing Homer is lower than the state’s standard for laying charges.
After all, the state has investigators and attorney generals and grand juries and congressional panels and other apparatus for deciding whether to pursue a case in court.
We only go after Frank is he was truly reckless, not just on the basis of whether the state can meet the very high bar of proving the case in court.
People get this very badly wrong when it comes to accusations of sexual misconduct or rape from long ago. The standard for a person accusing another person is much lower than the standard for the state obtaining a conviction in court, and that is as it should be.