That seems awfully unreasonable. Maybe this is some school policy.
This doesn't make sense, I mean I know that professors drop students who do not sign in the first 2 weeks of class, but they DROP the students. Because its during the first few weeks and before the deadline to drop without a W, they do not even get a W, much less an F. You never get a grade because you were never there. Getting an F would mean you DID attend the first 2 weeks because in order to get an F you need to be enrolled in the class and in order to be enrolled you would have to be there the first few weeks. Maybe the professor just hates you.
I always make sure to ask if the professor took attendance if I am not sure because people are often retarded and do not pass the sign in sheet around.