It's got to be something else you did, because the UV map will not effect the geometry of a mode other than where the texture shows on the model, it's physically impossible.
Actually, i just noticed ...
Remove doubles isn't anything to do with UV maps, what it does is merges any vertexes on the model that overlap each other. It may be that the boolean you used created extra geometry between loose vertexes, and that's why it fixed it.
But the odd thing there is what i showed you previously worked 100% exactly as i did it for me on your model maybe converting it to obj then importing it fixed some of the broken geometry, next time might be better off supplying the .blend file rather than an exported model, that way we can see clearer.
Give me a shout any time if you need any more help with blender.
P.S. With regards to modifiers ... ALWAYS apply them before exporting, the tick box for auto applying modifiers doesn't always work, always make sure you physically apply them. Also Some game engines don't like Blenders boolean modifier, even after it has been applied, no idea why, but it's a common complaint.
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