Okay, it looks like we received mixed messages from the OP. The OP mentioned an "accessible route" but then states the code official is concerned about accessing the elevator in the nonsprinklered building, which leads me to believe the code official is concerned about an "accessible means of egress."
Whether part of an accessible route or accessible means of egress, there is nothing to restrict this particular situation.
Regarding accessible route, the accessibility standards consider a building divided by fire walls as a single building, provided the accessible route connects all accessible elements of the building--even if that accessible route begins in one "building" and goes through other "buildings" separated by the fire walls. In the 2018 IBC, Section 503.1 was modified to state that the use of a fire wall was for the "purposes of determining area limitations, height limitations and type of construction." Thus, for all other purposes, a building divided by fire walls is a single building.
Regarding accessible means of egress, the elevator is only considered an accessible means of egress when determined by the design team for buildings less than five stories. If the building is five stories or more then the elevator must be used as an accessible means of egress. In this case, the building is only two stories, so the designers can elect not to make the elevator an accessible means of egress. The fire wall does meet the requirements for a horizontal exit, as previously mentioned, so disabled occupants can egress through a door in the fire wall and are considered to have "exited" the building. For occupants egressing from the sprinklered addition, the existing building is a refuge area. For disabled occupants, they can use the stairs in the existing building as part of an accessible means of egress, but there is no requirement to have an area of refuge for the stairway (Section 1009.3.3, Exception 6) and there is no requirement that the stairs have a clear width of 48 inches (Section 1009.3.2, Exception 2) even if though the building is not sprinklered. If the elevator will be used for the accessible means of egress, then it must comply with the requirements of Section 1009.4.