If bitcoin is a share then so is fiat. They are both currencies, only one is tangible and one is digital. In some cases bitcoin can be tangible, but in general fact stocks are simply owning part of the company.
You own a share you own a part of a company, you own a bitcoin you own a piece of currency like you do with cash.
This is a much more accurate description of what bitcoin is then how the OP describes bitcoin.
Owning bitcoin is like owing dollars, or euros, or yen. It is a currency.
it may be more accurate than OP's statement, but it's not the full story. it's like owning a currency and commodity (investment) rolled into one. there needs to be a new word for it, because that goes over most peoples' heads.