DC wiring confusion

[D-A]

Hello! Very new to this. I've been on site for days learning & seeing things! Thanks!

95 Medalist 36 v, given to me by nursery owner w/ Textron 3 charger. All batts DOA. Had charger checked, arced when they tested it. They said the wires (Blk. was on pos. & Wh. was neg.) were wrong, that white is always positive in DC. The DC cord was switched out, end is now-Wh. is pos. & Blk. is neg.

Here is my confusion- the cart plug (receptical) has the white as neg and the black as positive. I traced the white wire to the solenoid (I think it's the solenoid, small chrome like can mounted on the heatsink in the controller area with 4 bolts sticking out) then to the positive battery connection.

So is the wiring wrong on the cart receptical? Should I switch the white wire to pos. and the blk. to neg.?

I'll try to attach pic! Also have looked at web manuals and there isn't enough info for me to completely understand the wiring.