If you check the FEAT response you'll see:
Code:
MDTM
MDTM YYYYMMDDHHMMSS filename
which indicates the server supports both retrieving and setting of file times. The plain MDTM (which is perhaps all they are looking for) is an older RFC standard command to retrieve the file time. The second is a newer proposed extension RFC and they may not be using this.
They did check for the MFMT command which is another proposed extension to set the modification time of a file. ioFTPD currently doesn't support this so that's most likely why it thinks it can't be set.
Just to make sure it isn't a permission issue, use Flash or something to upload a file and enable the set timestamp on uploaded file feature in it and see if the server accepts the timestamp change. If it does then that software must only use MFMT and that isn't support so you probably can't sync the timestamps right now...
You could see if they support any other methods to change the timestamp like via one of the site commands that some servers use, that could always be easily scripted and added to the server.