Well, I realized that I was trying to add a file reference to a Copy Files Phase instance, which doesn't have a file reference collection. Instead, it has a build files collection.
So I modified the code as follows:
set aBuildFile to make new build file with properties {build phase:aCopy, compiled code size:0, name:aName, file reference:aFile, target:aTarget, comments:"", project:aProject}
add build file aBuildFile to aCopy
Note, these are header files I'm adding to the copy phase. However, now I get internal errors in Xcode during the call to "make new build file":
File: /SourceCache/DevToolsBase/DevToolsBase-620.0.81/pbxcore/PBXContainerItem.m
Line: 75
Object: <PBXBuildFile:0x06d401d0>
Method: setProject:
project should be an instance inheriting from PBXProject, but it is <NSNameSpecifier:0x08a1d1e0>