There are a bunch of things that could be at work here. Maybe the bitrate is too high. Maybe the flavor of h.264 is slightly different. Maybe the camera needs the EXIF data to be embedded in order to play it. Maybe the camera writes the files to the card in a certain region of the data blocks in order, and copying it to the card puts it out of order.
There’s a reason us naysayers say nay. You may “know” that there’s a workaround, but you really don’t–you hope there’s one. There’s probably a way to do it, but is worth all the time you’ll spend screwing around with it trying to figure it out? Why not just use one of the many options available to you BESIDES this, like playing it back from a computer, playing back directly to a TV via mp4 on a USB stick, pushing out a Blu-Ray disc, using an Atomos recorder, using an Apple TV…the list of really great, proven, useful playback technologies goes on and on. Playing back from the camera is not on that list.
Perhaps if you could shed some light on the intended venue and available playback apparatus, some of us naysayers could give you some helpful advice, rather than just telling you that your proposal is unlikely to work 🙂 What are you trying to accomplish? Maybe we can help you find a better solution.