So my argument for her or him, he or she, rather than they, is that her or him, he or she, in documentation humanizes the documentation. It piques my interest. There is an active person here.
It's not boring, dead trees, produced for some deadline documentation, Sally is doing something with this code! Bob needs to stop sending data!
He or she are far better to see in code comments for the same reason it's fun to encounter latin, or star trek quotes, or even curses.
They doesn't have that effect on me. They tells me the documentation was done grudgingly, likely by a prig. It is likely formally correct and will still say nothing, or be completely obtuse and thick.