Snapshots are private by default, you have to actively make them public (impossible if encrypted) or share them (which also requires sharing the associated keys if encrypted.)
Now, AWS hasn't wrapped the extra layer of “by default, reject any setting or policy allowing public or cross-account access unless separate additional default switches have been toggled off” thing to EBS that they have to S3. But people still expose stuff via S3, so that's hardly a panacea. At some point, one has to conclude that customers are responsible, in many cases for giving too many(or just the wrong) people admin access to their accounts.