if (user_can($id,'administrator')) 

http://codex.wordpress.org/Function_Reference/user_can

The Codex has a warning about using role names with the current_user_can function and it is very similar to user_can so I suppose caution is order until the conflicting instructions are sorted.

Do not pass a role name to current_user_can(), as this is not guaranteed to work correctly.

The same page also says:

$capability
(string) (required) capability or role name
Default: None

As does the source:

• @param string $capability Capability or role name.

Your question seems to boil down to this

I can't figure out how to check that the $userids in question are an administrators user ID.

Try

user_can($id,'administrator')

http://codex.wordpress.org/Function_Reference/user_can

The Codex has a warning about using role names with the current_user_can function and it is very similar to user_can so I suppose caution is order until the conflicting instructions are sorted.

Do not pass a role name to current_user_can(), as this is not guaranteed to work correctly.

The same page also says:

$capability
(string) (required) capability or role name
Default: None

As does the source:

• @param string $capability Capability or role name.

Are you hacking core file? The users.php isn't this users.php is it? That is a high maintenance path your are going down if it is.