This isn't true. When you log onto a machine the initial shell is run under
the logged-in user context. Any programs that are started within that shell
will also have the same user context. This can be overridden of course with
the RunAs mechanism in which you would supply the appropriate password for
the user account you choose to use. Services on the other hand are run under
the account they are configured to run with. Usually this is the local
system account, unless they are changed from the default where possible. If
a worm comes in via a service it will run under the user context for which
it gained access. For example with IIS this would be IUSR_MachineName if it
gained access with anonymous access. If the worm then takes advantage of a
buffer overrun exploit, it basically overwrites code in the memory space of
the program it is exploiting and would then be running with the rights of
that program. If you look at some of the IIS exploits for example, they
overwrite code into the memory space of the initial IIS process which
effectively gives them local system rights. This is why much of the malware
written leverages buffer overrun vulnerabilities.
Any program running on the machine such as a worm has the same security
context/rights as the user who is logged on the machine at that time.
You have to look at each piece of malware individually. Some go after buffer
overuns which will generally give them the rights under which the service is
run. Some propagate via network shares in which they may or may not try
using the user the account and password they are currently running under,
and/or may or may not enumerate user accounts and shares and try to guess
passwords for enumerated accounts and/or shares, and/or may simply guess
passwords while using the default administrator account and default
administrative shares. And so on and so forth.
This is not really true. When you join a machine to a domain the Domain
Admin group is added to the local machines Administrators group. You can
take the group out or move it to a different local machine group if you
wish. There are also changes made to the local computers user right
assignments which again you can modify. You could for example deny Domain
administrators the right to log on locally however allow remote access, or
deny both local and network access.