It's not an assumption-it's a consequence of the CPT theorem, that, in turn, is a statement in quantum field theory, cf. http://tpcsf.ihep.ac.cn/TALKS/peccei.pdf for a presentation that has been *tested* experimentally (one doesn't ``prove experimentally'' anything), e.g. http://neutrino.ethz.ch/Positron/poswor03talks/felcini.pdf
which means, that the assumptions of the theorem have been tested.
If there were any measurable difference, it would be an indication of Lorentz violation, cf. http://www.physics.indiana.edu/~kostelec/faq.html