When running a Synology, take care when you require (or don't want) public (a.k.a. guest) access to shares.
To allow access, first check whether the guest account is not disabled. I found out it was disabled after joining the device in a Windows domain. Disabling the account is a good way to effectively cut off all public access.
If you require guest access on some shares but not on all, be sure to set the ACL for Guest in Privileges Setup to No Access for shares that have to be locked down. Not explicitly setting this will allow public access on that share.