Well, thats quite a conundrum. From a supervisory stand point most of the problems a department has is due to attendance. HR erred by even letting your file get to the interview stage, so now they are kind of stuck. What I would personally do, would be to allow you to come onboard with the condition that you not miss any days of work for set period of time, maybe in excess of the standard attendance policy. Now I would be reasonable, if you were somehow were to be injured or exposed on the job that would be the one exception. Once you have shown that the past discretion is not likely to repeat, I would treat you like any other staff, as a valued member of the team.