What do you mean it isn't true? It's a well known fact. It's just a proton and an electron, so it's absolutely tiny. There is almost no way to seal it perfectly, especially in gaseous form. It's always going to leak. Even for rockets this is an issue. You can make that amount relatively small, but it pretty much always has some loss.

Caverns may make sense for large-scale solutions, because the quantity is so large compared to the loss. Most people don't have massive caverns under their house though, nor do they have a need for that large of a quantity.