I think that this procedure can be seen essentially as a classical acid/base diphasic alkaloid extraction. The only thing that is missing is the nonpolar solvent at the end to separate the freebase alkaloid from the aqueous phase. Unfortunately, with many alkaloids, the nonpolar phase really is integral--it just can't be omitted. The problem with crystallization of some freebase alkaloids is that the crystals can be hygroscopic, so even if the alkaloid isn't all that soluble in water, some water will adsorb, making it difficult to end up with good, firm/solid crystals (instead, you end up with more of a mush/goo that takes a long time to dry out). Hence, solubilizing a freebase alkaloid is a nice dry nonpolar solvent helps one end up with solid material, rather than paste.
I believe the only reason that hydroxide was specified in the first place was to prevent having to do a classic two-step extraction procedure. I mean, if you don't want to use a hydroxide base, you certainly don't have to: just extract first with an acid (personally, I'd use something other than acetic acid, as it smells like ass), then basify with anhydrous sodium carbonate and then add the nonpolar solvent. Additional sodium chloride can be added as well, as a phase-transfer catalyst (goal is to make the aqueous layer as polar as possible, accelerating the transfer of the freebase).