Attempting to pull a single file using
adb pull /data/data/com.corp.appName/files/myFile.txt myFile.txt
fails with
failed
Does that mean that one could chmod the directory from world:--x to world:r-x long enough to be able to fetch the files?
Yes, exactly. Weirdly enough, you also need the file to have the x bit set. (at least on Android 2.3)
chmod 755 all the way down worked to copy a file (but you should revert permissions afterwards, if you plan to continue using the device).