Does the scope for 'Alter Any Database' operate similar to 'Create Any Database'?
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.