I have a custom approval process that goes through 5 teirs of approvals, based on the discount of the quote and the level of the person.  The problem is, when the first approver tries to approve the record, i get the following error:

Validation Errors While Saving Record(s)
There were custom validation error(s) encountered while saving the affected record(s). The first validation error encountered was "Apex trigger ApprovalProcessHandler caused an unexpected exception, contact your administrator: ApprovalProcessHandler: execution of AfterUpdate caused by: System.DmlException: Process failed. First exception on row 0; first error: NO_APPLICABLE_PROCESS, No applicable approval process was found.: []: Trigger.ApprovalProcessHandler: line 83, column 1". 

line 83 is just : 
Approval.ProcessResult result = Approval.process(req);

and req is defined as: 
Approval.ProcessSubmitRequest req = new Approval.ProcessSubmitRequest();
                        req.setComments('Submitted for approval. Please approve.');
                        req.setObjectId(tQuote.id);                        
                        req.setNextApproverIds(new Id[] {tUser.id});

This doesn't make sense to me because the last approval process in the list has an entry criteria of "TRUE" which means every single approval process should his this step.  Also, when I give the approver modify all access to the record that is being approved, it works fine.  I don't want to give them modify all to the record though.  What is going on here? I didn't think a user had to have privelages to submit a record for approval? (i've tried with locked and unlocked records, problem exists in both)