With a smartphone, when you are sent a message, part of that message (or all of the msg if it is short) can be seen on the home screen without opening the conversation, simply by looking at the display. Until the phone/message app is 'opened', the message will be shown as 'unread'.
(however, we don't know what phones were in use!)
OK, I stand corrected on that, same on my BlackBerry come to that, provided the message is short.
Having said that, the AAIB report only identified the last received text ("Yes it’s fine still here") as not having been read, unlike all the prior ones, including a couple that simply said "OK" and would therefore not have needed to be opened if a smartphone was being used, but were.
Although the message itself hasn't yet been sent, there will be traffic on the network to inform imessage on the 'receiving phone' that a reply is being composed.
Again, I think that's dependent on the phone, and maybe the network, and/or whether the AAIB were actually referring to IMs when they talked about texts. My BB certainly doesn't talk to the network when I'm typing an SMS reply, so I still don't think that scenario can positively be ruled out just because the network didn't record it.