The problem is that secondary libraries, that are not glibc, will not have multiply defined functions for different size of off_t and will not have the switch in their header file to transparently select the correct set of functions based on what the client program wants.

Yet, somehow the article emphasizes that this is more of a problem for time_t than off_t.

This is believable and it's brobably it's because time_t is more pervasive. Whereas off_t is a POSIX thing involved in a relatively small number of interfaces, time_ t is ISO C and is all over the place.

On top of everything, lots of C code assumes that time_t is an integer type, equal in width to int. A similar assumption for off_t is less common.