All checks are done using the context of the user running Servers Alive.
So if you're running Servers Alive as service (using the system account with desktop interaction I would presume), the checks are done using the credentials of the system account.
The system account of host_1 has no rights on host_2 and worse you can't give rights to it. Does this mean that you can't correctly check services/processes/diskspace on remote NT/Win2K systems when Servers Alive runs as a service? No! You can specify a username/password combination for each of the checks. (make sure that if the host you're checking is part of a domain to include the domainname within the username -> domainnameusername)