They'd likely argue to use natural keys instead. Use the data that matters to you, index it across more than one column.
For cases where one sensibly used uuids, I don't see natural keys being an alternative. What's e.g. the natural key of an order reference that should be accessible without auth, when the key shouldn't allow enumeration and that should be allocatable without a single point of coordination?
Those users were very wrong, unless they explicitly only talked about the case where the uuids are not indexed.