The fact that two expressions denote the same object does not mean that they are identical in meaning. For example, consider "Venus is the morning star" and "Venus is the evening star". It happens only one heavenly body is involved, but it required empirical science to establish that "morning star" and "evening star" refer to the same object.
If you were translating from English into Czech, would you use the same words to translate "My sister is short" and "My sister is not tall"? Do they "mean" the same thing?
Of course two different wordings represent (usually) two different shades of meaning-- otherwise we wouldn't bother having them. However, here the issue is what is the appropriate translation of Mam jedno vejče, and we have no choice but to respect the view of Czech experts who tell us which is the best translation. If I knew, I would not be on DL.. ;-) I would not get here into a philosophical exploration of what MEAN means, either. Deciding when to use the Genetive case is difficult enough...