I'm not sure about the reference to school friends?
He trusted them as much as he trusted anyone in that business. The Don was a very cautious man and wanted to ensure that only he (and perhaps Genco/one of the Don's sons) had the big picture about what was going on.
So this means that Clemenza doesn't need to know what orders the Don gives Tessio and vice versa. Also both men together control almost of the Family's soldiers so the Don didn't want them to be too chummy with each other or get ideas about making changes at the top.
"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming
Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.
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