The attack presumes your home directory is client side, and you use SCP to connect to any kind of server, whilst ~ is the client side open directory.
Thus, any server you might SCP to could write to your local home dir. In university, I did this with compute clusters, servers of my association and other servers.
This breaks the SCP security model because it means a server has covert access to your local working path. Whereas normally you know which files SCP touched, so you can verify they are as intended.