Patrick’s Unique Identifier Dictum (PUIDD): If you need to assign unique identifiers in order to differentiate two records in a database, you don’t need to differentiate those two records in that database.
(No, this is not always true. I think the ratio of how often it is true to how often informatics people believe it is true, though, is very high. It’s at least worth asking what a UID is intended to accomplish in any particular case, rather than assuming that they are universally desirable.)
Taken literally, if you would need UIDs to distinguish two records, you can’t differentiate them. But this is too obviously tautological to be useful.
UIDs are useful insofar as they serve as reliable proxies for other differences between the records that it would not be practical to use directly.