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.