I haven't ever actually used APP, but I don't have problems with
it not having any parents.
APP is a member of %m.edit;, which in turn is included in
%m.phrase;, which in turn is included in %m.paraContent; (among
others). Thus, APP can go most anywhere. It is interesting to note,
though, that the P3 text lists "[none]" as the "May occur within"
for APP (p. 864).
I have successfully validated a file with an APP inside a P
element using Author/Editor on the Mac.