The sad part is that your government ID is about as likely to be leaked by the government agency itself than it is by any third party that has an scan of it.

My driver's license is scanned every time I buy beer. I'm under no illusions that it's not quite readily available in any number of leaks or disclosures.

If that sounds defeatist, maybe it is. Nothing online is private. Once it's in a database, it's only a matter of time before it's exposed. History has proven this again and again.