Well this is what my friend told me. I trust his reading abilities. Maybe he's a little off, since his translation skills aren't great but I'd like to believe it's closer.
Well, つけっぱなし is 付ける, to attach/wear, plus っぱなし, to keep X-ing or remain in a state of X-ing (where X is a verb stem). Even if your friend somehow misinterpreted that つけ to be the stem of a verb meaning "to take off" (which it isn't; "to take off" would most likely be 取る or 外す), っぱなし certainly doesn't have any connotation of "let's".
Thanks for not changing the note, at any rate. I would certainly be interested in hearing the rationale behind your friend's interpretation.
