"Frustrating Policy on Lateness"

I was two minutes late to an appointment today, meaning that the automated system to sign in would not let me do so. Waiting in line for the receptionist then meant that I missed my appointment entirely.

Would it not be possible for the automated sign-in system to allow you to sign in if you are only a few minutes late to an appointment?

I would not be so annoyed by this if it weren't for the fact that last time I attended an appointment, my doctor was more than half an hour behind schedule. It is hard not to feel that there is a double-standard here.

I would not expect to be seen for the full length of my appointment given that I was late, but it is extremely frustrating that I could not have seen my doctor for the remaining portion of my appointment (which was most of the appointment) given that I was only a late by such a small margin.

It is only because the automated sign-in system would not let me register that I missed my appointment altogether. Is there any way that the automated sign-in service could be altered to make this possible?