There is nothing written about being like a commlink and giving access to the matrix. It only gives better values and response.
I was just talking with a friend about this yesterday! I agree with you that it is unclear, however I think the rules seem to fall on the side that a commlink is not necessary if you have a cyberdeck. That is:
commlink --> cyberdeck
datajack --> cyberjack
in terms of decker "upgrade". I base this on the fact that in two key places the phrase "commlink or deck" is used. One is on page 176 under Dumpshock/Linklock, and the other is on page 178 under Running Silent.
Its definitely unclear, in my opinion, but the above was our interpretation.
To be clear, I think a decker still probably needs a commlink, but that would be for at least some of the other features a commlink provides, e.g. (pg 267)...
telephone, vidphone, text,
music players, micro trid-projectors, touchscreen
displays, high-resolution video and still-image
cameras, image/text and RFID tag scanners, built-
in GPS guidance systems, chip players, credstick
readers, retractable earbuds, voice access, and text-
to-speech and speech-to-text technologies.
Its really not clear which, if any, of those things a cyberdeck provides beyond just connecting to the Matrix.
Also, I acknowledge this is not directly on-topic to your question, so sorry to derail, but it seems important to your question.