iTunes Match is in use and the file is already in the cloud
iCloud Music Library is in use and the file is already uploaded
There could also be other reasons like the file was purchased by a different Apple ID, especially if it is an older "Protected AAC" file. You can manually add the song, play it and enter the password for that Apple ID to allow it to play.
Other possibilities are it is a file that is not supported, like a text file or a corrupt AAC file. Not much can be done with this, other than replacing a corrupt AAC file with a good one.
I've just found some info that only files from iTunes Store (or imported into iTunes library using the AAC encoder) will be played in iTunes.
So the only option is using third party software to convert AAC files to any other format playable by iTunes.
Anyway, thank you.
iTunes can play audio formats MP3, AAC, AIFF, WAV, and Audible aa, all can be created with 3rd party software. There is also iTunes audio formats like m4a (AAC), m4b (AAC), m4r (AAC), m4p (encrypted AAC) and Apple Lossless.
If the MP3 is encrypted for another player, iTunes cannot play it. Just like the reverse, iTunes encrypted AAC files cannot be played by other AAC players.
I actually meant:
"I've just found some info that only AAC files from iTunes Store (or imported into iTunes library using the AAC encoder)..."
The AAC file (a radio podcast) I have been trying to import into iTunes is played by all other players but not iTunes.
Some advised to change the extension from .aac to .m4a but that didn't work, either.
So I could only resort to using 3rd party software to convert to MP3. And the converted files are accepted by iTunes.