Most toilets I've used don't fill the bowl with enough water on a single flush to overflow. You can adjust the chain (assuming not an office toilet) if it's flushing for too long.
The only times I've overflowed a toilet I was as a kid, not realizing that trying to flush again might make the problem worse.
I assume either they mean they don't keep flushing it over and over if the bowl fills up or their toilet flapper has a short chain and stops flushing quickly when they let go.

It doesn't say when they told Wikipedia about the paid editing, but once Wikipedia investigated it they banned them and denied the appeal. The account never came back to make more edits after they were discovered.