What? No, that's not how batteries work. They don't have "more space", they just use a shitty cell chemistry. Yes, there are cells that are designed for high current and use a cell layout/chemistry optimised for that instead of high capacity, but those crappy cells definitely aren't.
Also, your 20 A figure is VERY high for good cells and catastrophically high for that crap. As you've said yourself, that would be a 20 C discharge for those. LG/Samsung cells are normally rated for 10-20 C, i definitely wouldn't use more than 3-5 C for untested garbage.