In NaCNBH3 in MeOH, the proton from the alcohol can provide a proton, but your starting amine looses a proton once the alkyl group attaches, so you ultimately are just shuffling protons around, not really creating or losing them. You may also create a trace of NaCNBH2OMe, which would release some water to the reaction. And when you form the imine, you release water in any case, which provides protons for future needs. I still find that in many cases a drop of acetic acid helps the reaction, but it is case and substrate dependent.
In the triacetoxy case, there is no need for acid, as the borohydride is already weakened so much in reducing ability.