This approach most likely requires that the script runs within the same trusted local network, correct? So, technically you'd still have to "ssh" into at least one box, and run all admin scripts from it.
Generally speaking, your servers will be bound to the same Active Directory domain, so if you're logged in via AD, and AD says you're an admin on the boxes you're trying to hit, you're good. This is called trusted authentication, and is similar to forwarding your SSH agent all over the place.
That opens up what happens if you're not in the domain (say, you're on your home laptop). Many commands take a -Credential parameter, which takes an authentication token available that you create via Get-Credential. If the command you want to use takes -Credential, then you can still avoid actually logging into the remote machine in the way you would for, say, SSH.
If, on the other hand, the command you want doesn't take -Credential, you do either need to use Invoke-Command, or genuinely log onto the remote PowerShell service via New-PSSession/Enter-PSSession, which is an extremely direct analog for SSH.
Note that Windows 8 removes the distinction between Pro and other editions.