Why is permission denied during pssh?

I am trying to add an ssh public key to a bunch of servers authorized_keys file. My thought was to use pssh and a list of hosts. To test, I tried to pssh to one host:

pssh -i -H root@host echo mypublickeyasastring >> /root/.ssh/authorized_keys

When I run this, I get:

-bash: /root/.ssh/authorized_keys: Permission denied

If, from the same server I run pssh, I just ssh into the host ssh root@host, I get in okay and I can run echo mypublickeyasastring >> /root/.ssh/authorized_keys just fine.

I've been skimming the pssh man page but I can't seem to find anything. Am I missing something? Is there a better way to do this?

The output redirection is happening on the local machine. You need to quote the command to protect the >>.