The 15v minimum PS business is invoked only in referring to charging "high voltage batteries at high current (charger output 250watt)" and they spec the PS should be rated for 350watt (or more) which is 23.3a "to insure reliable performance".
This prob refers to 6S lipo charging at 10a - 0610i max capability. Thats 25.2v minimum when it ends the CC part of the charge and 252watts. So for a PS thats 13.8v, its pulling 18.3a output for the same power - seems like even a good 20a supply should be capable of doing that. Note these are continuous amp ratings, not maximum.
Maybe they're being cautious - product liability concerns??. I charge 6S a123s at 10a and my 13.8v 25a PS never shows any sign of distress. Fan cycles just like it does when I'm charging a 1600 2S at 1.6a. I saw that in the manual, but am not real concerned about it, more of a curiosity.