I don't think a good definition of custodian is "can steal your money". Trust and custodianship are not the same thing. Trust is a superset of custodianship.
Imagine you have your gold bullion in your house. Your neighbors know. They COULD shoot you and take your gold. You're trusting them not to. That does not mean your gold is custodial, IMO.
Ronald Reagan said in a speech once that the reason for government is so you don't have to walk around with a club. And that's where I think the difference is: on the internet, you do. If you just "trust" people on the internet not to collect your information (that's all bitcoin is), you will be had. Cryptography is the club that deters them. And that is why, when it comes to bitcoin, if someone on the web can steal it, it's actually custodial. It's in their possession. If they have a "send" button and can push it without you, I recommend you consider it not really your money -- consider it theirs.
reply
if someone on the web can steal it, it's actually custodial
Hard disagree. The legal definition of "custodial" generally refers to a situation where an individual or entity is responsible for the care, supervision, or safekeeping of another person or property. There's a lot of things that would fall under your definition of custodial that are clearly not, such as someone generating a private key with one dice roll. Who is the custodian here? Someone on the web can steal it.
reply
The legal definition of "custodial" generally refers to a situation where an individual or entity is responsible for the care, supervision, or safekeeping of another person or property
Just replace the verb with "has":
The accurate definition of custodial is a situation where an individual or entity has another person's property
such as someone generating a private key with one dice roll. Who is the custodian here?
reply