That's one possible analogy. Another analogy would be: an unrelated third-party decides to give, to everyone who has HP shares, an equivalent number of shares in a new company. In that case, a broker would be under no obligation to give you these new shares.

Which analogy is the best one depends on your point of view on this debate.

> a broker would be under no obligation to give you these new shares.

No obligation would exist, but I'd rather take my business to a broker who would do so, given the choice.

How about a third-party company that awards a free trip to a timeshare resort (some obligations apply) to every HP shareholder?

Correct. I have not studied securities law but I don't think Coinbase's users have any recourse claiming their BCC and Coinbase decides their stance is that it was always theirs as they held the relevant private keys.

This analogy doesn't work because people could've transferred their Bitcoin to a personal wallet while the same can't be said of stocks.

Actually... with many brokerages, you can still obtain actual paper stock certificates -- it's just that the overhead and fees to do that make it highly unattractive.

Furthermore: It is possible to directly transfer stocks from one brokerage account (similar to a wallet) to another at a different brokerage without having to liquidate assets.