Yes, money is any item or verifiable record...but record of ownership
Nope. Not verifiable record
of ownership.
Any verifiable record
that is generally accepted as payment for goods and services and repayment of debts, in a particular socio-economic context.
everyone is free to view them as money and trade their property for them, but that's irrational as they are worthless.
It isn't worthless if it is
generally accepted as payment for goods and services and repayment of debts. All commodities (such as gold) or anything else that has "ownership" are also worthless if nobody is willing to accept them as payment for goods and services and repayment of debts. Value is an intrinsically human concept. If humans desire something (membership, ownership, or something else entirely) then it has value. If humans do not desire it, then it does not have value.
Regardless, A Bitcoin private key is proof of "ownership" and not "membership". It is possible to "own" rights to value, which is what a private key provides.