My first reason to “shred” documents (that is to look closely at each statement a source makes) was that it forces you to be aware of the details. The second reason to shred documents was to allow you to get a sense of the truthfulness of each statement on its own merit.
The third reason to shred your documents is that you will see connections between bits of information from separate sources only if you are really conscious of those bits. Imagine that you are trying to tease apart “your” Smiths from the other Smith families in the county but they all seem to use the same first names so even Robert Smith son of John Smith could be any one of three people. You’ve got a tough problem. What though if you’ve “shredded” your documents and you notice that a large number of the county’s land transactions involving Smiths also involve men with the surname Schwarzwalder. Now you can start to wonder of one of those Smith families is related to the Schwarzwalders somehow and the other Smiths were not related to them. You have a testable hypothesis. It might be wrong but right or wrong it will give you a way to think about your problem that you didn’t have before.