Indeed, the proposed mechanism in the link, seems complex, weird and exotic.
In my opinion, it is acidic catalysis because phosphine behaves as Lewis acid catalyst by complexation with the alcohol, in a similar way as with amines; which can also explain the H/D exchange, when deuterated alcohol is used.
Nevertheless, it is more convenient to add a catalytic amount of phosphine than preparing and working with a catalytic amount of t-BuOK, even if obtaining a little lower reaction yields.
1). New synthetic opportunities using Lewis acidic phosphines, Journal of the Chemical Society, Dalton Transactions, (23), 4307-4315, (2002) https://pubs.rsc.org/lv/2002/dt/b208715d
2). Nitrogen Ligands on Phosphorus(III) Lewis Acceptors: A Versatile New Synthetic Approach to Unusual N−P Structural Arrangements, Inorganic Chemistry, 42(4), 1087-1091, (2003) https://pubs.acs.org/doi/full/10.1021/ic026090l