Freeware Advanced Audio Coder

The bug is in the application you use for playback. It assumes a file with
audio only will have "M4A " in the file type description, and assumes files
without that to have video. This is a false assumption. The player should
check what kind of track types are in the file to draw any conclusions.

Oops, this one is present in both. Here goes the relevant output from
mplayer's movinfo tool:
--- itunes.log 2007-11-21 19:29:53.000000000 +0100
+++ faac.log 2007-11-21 19:24:19.000000000 +0100
@@ -1,3458 +1,18609 @@
position atom (atomtype) len [human readable atom name]

-00000000: ftyp (70797466) 00032 [unknown] (begin: 00000008)
-00000020: moov (766F6F6D) 16985 [Information sections] (begin:
00000028)
-00000028: mvhd (6468766D) 00108 [Movie header] (begin: 00000030)
-00000094: trak (6B617274) 14113 [New track (stream)] (begin:
0000009C)
-0000009C: tkhd (64686B74) 00092 [Track header] (begin: 000000A4)
- Flags: 7
+00000000: ftyp (70797466) 00024 [unknown] (begin: 00000008)
+00000018: mdat (7461646D) 6627118 [Movie data] (begin: 00000020)
+00651F46: moov (766F6F6D) 75049 [Information sections] (begin:
00651F4E)
+00651F4E: mvhd (6468766D) 00108 [Movie header] (begin: 00651F56)
+00651FBA: iods (73646F69) 00024 [unknown] (begin: 00651FC2)
+00651FD2: trak (6B617274) 74748 [New track (stream)] (begin:
00651FDA)
+00651FDA: tkhd (64686B74) 00092 [Track header] (begin: 00651FE2)
+ Flags: 1

Movie header (mvhd) one is also present

This might be due to the fact that the generated files apparently contain
an empty movie data (mdat) atom.

The MIME types reported by nautilus and file outputs are the following:
faac: video/mp4; ISO Media, MPEG v4 system, version 2
iTunes: audio/mp4; ISO Media, MPEG v4 system, iTunes AAC-LC

This happens with both internal and external libmp4v2.