"Position invariant" is a vertex program option that ensures rasterization with vertex programs occurs exactly at the same place at the geometry would with the fixed-function pipeline. With this option, you're free to render the same model with and without vertex programs in the same frame while preserving depth-buffer rasterization (thus eliminating Z-fighting). It's a must-have for multipass rendering.
Historically, John Carmack advocated for this option. Without him the option would certainly not be in the spec. For that, I guess many programmers do thank him today.</history>