Tough call...I had stage I private check students who could land the aircraft three times to syllabus standards, but still had a 'gut' feeling that was almost always luck.???...
you have no solid proof other than a 'gut' feeling....
how are you going to sign him off for his first solo or an additional endorsement? or for a checkride knowing in your gut this student is a thief?...
To me, if someone didnt pass the gut check, i.e. it was luck or, man that was barely passable....they didnt get by. Your guy in my opinion is outta there!!!