The compatibility issue with MS type connectors mentioned in the OP is quite common. I own several lamp with the MS type connectors and like the OP some do not make as tight a connection as others. All of them though do work. Usually the problem is with the ( male ) plug on the lamp. On some of those the outer part of the plug is not as wide so it doesn't connect as well with the outer sleeve on the female side. On other male plugs the metal shaft that connects to the battery ( female ) side isn't quite as long as some others thus preventing the outer part of the male plug from connecting tighter to the battery side.

I've never had one of these become unconnected while riding but I'm sure it could happen. Nothing that a piece of electrical tape can't fix but if you want a better connection you could try replacing the male plug with another better version. You can buy the MS type extension cables, cut the male side off and splice the better plug in. It does require some minor DIY skills but can be done without too much trouble.

Anyway, I can't see returning the lamp because it won't work well with other batteries. If it works with the provided battery you got what you paid for.