When you have a huge speed effect (the one you can aquire using commands, not potions), then when sitting in minecarts, the player renders flying on top of it, not being in the minecart. The bigger the effect the bigger the distance between the player and the minecart seems to be.
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What is an example of an effected amplifier?

I don't know exactly, but it occured on this minigame, when I clicked the "adventure" button: http://bit.ly/1j1Rq9Z. When going to "adventure" in that minigame and then going into the minecart, I became glitched out.

Confirmed with the linked world.

What amplifier was that? You can check by exiting with the speed boost and reading level.dat
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Amplifier 8

Thus duplicate of MC-10755