It's interesting because I've never heard of this problem yet almost everyone I know owns a 360 and I have to assume most of those people have the plug and play charge kit since it's awesome (or I had thought it was).
I know my controller is starting to do funny things where I'll charge it but the guide lights start flashing at two bars left on the battery but I assume that's because the battery is old and has been recharged many times.
I'll have to try that removing the cord trick.