It performs a QR decomposition! I think, but am not entirely certain, because QR is somewhat more stable numerically than Cholesky. The fact that it doesn't perform exactly like one of the others is because it doesn't use the R functions, but is written in pure C with barely any checking.
Comments
The key difference from LINPACK (in src/appl/dqrdc2.f) is that it pivots only when really needed, so that computing sequential "this beta adjusted for the previous ones" is more straightforward.
I get why this is the sensible default ofc, but it seems reasonable to offer other methods given modern dataset sizes.