Rental dispute with the tenant

[Karl Forshee]

so I'll do my best to condense the situation down.

Last September I got soft hearted and agreed to a renter who had been down on his luck  (ya I know don't think with the heart) and that the rent was  going to be paid by the Idaho Housing Authority.  He applied in early September of last year but we didn't let him move in until the very end of of September as we wanted to make sure that Idaho agreed to pay on his behalf as nobody  could confirm until the check was cut. Idaho paid for four months of rent plus the deposit.  their letter specifically mentioned that the rent was for September, October, November and December.  

Go forward to December and true to form we get a notice that Idaho ran out of money in thier housing budget and they will no longer be able to continue the rent payments.  However, the good news is that the tenant was able land a good job and says he can continue paying the rent without issue.  The problem is he believes that since he didn't move in until the very end of September, he shouldn't have to pay until Feburary 1.   Our argument is that since we held the place from his application in September and that the rent was specified to be from September to December he should start paying the rent January  1.  We offered a compromise of him only paying half the rent in January but he is still refusing.  I have called the Idaho Housing Authority and they reiterated that the rent was from September to December. But, it's up to us the landlord to decide on how to proceed next.

So what are your thoughts on this matter.  Are we crazy?