Files are not read-only and updating tags is available.
Easily reproduced. I took one file and removed the cover art from it. I usually have "Next to file (artist - album.jpg)" but checked the "Store images in tags also" option. I did a quick find of the cover art and the image was put inside the file. The Image File tag said "Inside File" but I couldn't see where it was in the Format tag like you said:
MPEG-1 Layer 3
192 Kbit CBR
44.1 Khz Joint stereo
Copyrighted: No
Original: No
Protected by CRC: No
Encoder: <unknown>
Gapless: No
ID3v1 Tag: (128 bytes)
Name: Silver Spoon
Artist: Kiss
Album: Hot in the Shade
Year: 1989
Comment:
Track #: 8
Genre: Rock (17)
ID3v2.3 Tag: (10102 bytes)
TLEN (Length): 282880
APIC: <unknown data type>
TCON (Content type): Rock
TYER (Year): 1989
TPE2 (Band): Hot in the Shade
TIT2 (Title): Silver Spoon
TRCK (Track number): 8
TBPM (BPM (beats per min..): 127
TPE1 (Lead performer(s)): Kiss
TALB (Album): Hot in the Shade
USLT (Unsynchronized lyric): <too large to display>
COMM (Comments):
COMM (Tool Name): Media Center
COMM (Tool Version): 12.0.163
COMM (Artists): Kiss
COMM (Date): 32509
COMM (Peak Level): 0.96857
COMM (Replay Gain): -10.221
COMM (Intensity): 5
COMM (Styles): Arena Rock;Pop-Metal;Hard Rock;Heavy Metal;Album Rock
I unchecked the "Store images in tags also" option. I then said to remove the cover art and answered yes to remove it from the hard disk too. The Image field was now blank and the Format tag showed the exact same information as above. Just to verify the image was still inside the file, I used various tools like iTunes, WMP, etc. to load that one song. I thought there might be a chance they were downloading the image from the Internet but to verify that, I loaded one of the other songs that I knew didn't have Inside File and no cover art was shown in iTunes and the tags within.
So basically I am unable to remove cover art from inside the file.