I decided to redo my original answer as I didn't formulate my response to what the question specifically asks and I neglected to consider the intent of the "message forwarding system" language in part 97. My apology for any confusion from my first answer.
The following discussion specifically applies to amateur radio stations under FCC Part 97 regulations.
An amateur radio station may be locally controlled, remotely controlled, or automatically controlled as defined by part 97:
Local control. The use of a control operator who directly manipulates the operating adjustments in the station to achieve compliance with the FCC Rules.
Remote control. The use of a control operator who indirectly manipulates the operating adjustments in the station through a control link to achieve compliance with the FCC Rules.
Automatic control. The use of devices and procedures for control of a station when it is transmitting so that compliance with the FCC Rules is achieved without the control operator being present at a control point.
Any station may be locally or remotely controlled. Automatic control is the most limited form of control in that only certain station activities are permitted: auxiliary station, repeater station, certain beacon stations, digital stations and message forwarding stations.
It would be tempting to run with the automatic digital station concept for a node on a mesh network, but there are two major limitations that generally prevent this:
(1) The station is responding to interrogation by a station under local or remote control; and
(2) No transmission from the automatically controlled station occupies a bandwidth of more than 500 Hz.
In March 30, 1994 the FCC adopted PR Docket No. 93-85 in recognition that with the regulations at that time "the potential for transmitting a high volume of messages cannot be achieved" and they sought to add specific language and restrictions that allowed the transmission of high volumes of messages.
First, they added a new section defining message forward systems:
Message forwarding system. A group of amateur stations participating in a voluntary,
cooperative, interactive arrangement where communications are sent from the control operator of an originating station to the control operator of one or more destination stations by one or more forwarding stations.
Then they relieved all forwarding stations of most legal responsibilities regarding the content of the message:
(b) For stations participating in a message forwarding system, the control operator of the station originating a message is primarily accountable for any violation of the rules in this part contained in the message.
(c) Except as noted in (d) of this section, for stations participating in a message forwarding system, the control operators of forwarding stations that retransmit inadvertently communications that violate the rules in this part are not accountable for the violative communications. They are, however, responsible for discontinuing such communications once they become aware of their presence.
The originating station is primarily held responsible:
(d) For stations participating in a message forwarding system, the control operator of the first forwarding station must:
(1) Authenticate the identity of the station from which it accepts communications on behalf of the system; or
(2) Accept accountability for any violation of the rules in this part contained in messages it retransmits to the system.
PR Docket No. 93-85 also changed the definition of an auxiliary station and a repeater station to clarify that they are not part of a message forwarding system:
Auxiliary station. An amateur station, other than in a message forwarding system, that is transmitting communications point-to-point within a system of cooperating amateur stations.
Repeater. An amateur station that simultaneously retransmits the transmission of another amateur station on a different channel or channels.
The final significant addition resulting from PR Docket No. 93-85 was:
No station may be automatically controlled while transmitting third party communications, except a station participating as a forwarding station in a message forwarding system.
This is a key paragraph as this not only grants the right of a message forwarding system to pass third party traffic, but it also grants the right for a message forwarding system to be automatically controlled.
Finally, regarding your concern:
I also recall reading that an automatic control station may not initiate contacts, but only respond to a contact from an operator-controlled or remote-controlled station.
This language largely comes from the limitations of an automatic digital station. It does not apply to a station participating in a message forwarding system.