The painful technicallity is that "the checks will clear AT THE TIME YOU CALL."  If someone else's checks are posted to the the account say 30 minutes after your call or before your deposits make it through the clearing house and are posted, your checks may not clear.

NOT always possible in today's world:  In the old days, after making that call I would immediately go to the bank the checks are drawn on and pay to have them certified before depositing them into my office account.