Maybe it's too fine of a line, I think it's not exactly distrust of Clemenza that turned Santino to Tessio's men after the attempted hit, it's just simple prudent procedure. The lapse could have come from either sloppiness or disloyalty, but that was no time to find out.

I think that Hagan's remark that he would have expected Clemenza to be the traitor is out-of-character, and that it was made purely so that Michael could say something philosophical about how intelligence is a poor master.