Does the scope for 'Alter Any Database' operate similar to 'Create Any Database'? Does the scope for 'Alter Any Database' operate similar to 'Create Any Database', as in, only those databases created by Login-A under the 'Create Any Database' umbrella can be altered, and not the other databases on the server?
Why is this so hard to test for yourself? As sa or similar:

CREATE LOGIN Jake WITH PASSWORD = N'x', CHECK_POLICY = OFF;
GO
GRANT ALTER ANY DATABASE TO Jake;
GO
CREATE DATABASE IBelongToAaron;
GO


Now log in as Jake:

CREATE DATABASE IBelongToJake;
GO
ALTER DATABASE IBelongToJake SET RECOVERY FULL; -- success!
GO
ALTER DATABASE IBelongToAaron SET RECOVERY FULL; -- success!


So no, ALTER ANY DATABASE works as advertised, which is probably why it's not called ALTER ANY DATABASE THAT I CREATED OR OWN.