Does RedP+HI reduce all carbon functional groups to alkane?
Nope, in general it doesn't. You are correct. See also for example: 


A. Aramini, M. R. Sablone, G. Bianchini, A. Amore, M. Fanì, P. Perrone, A. Dolce, M. Allegretti, Tetrahedron 2009, 65 2015–2021. DOI: 10.1016/j.tet.2009.01.005:






M. Dobmeier, J. M. Herrmann, D. Lenoir, B. König, Beilstein J. Org. Chem. 2012, 8, 330–336. DOI: 10.3762/bjoc.8.36 Open access PDF. (This also includes your one as a reference, too.):





If it did, it would be a pretty poor reagent since it would have no functional group tolerance, so not very useful. However, it is not unlikely that under special conditions it might be able to reduce carboxylic groups as well.