There are large checklists that need to be completed prior to take-off, not sure how much of this is automated now but if that is no longer possible you're just not going to take off.
I've written fuel estimation software for 747 cargo planes for one particular airline. Pilot would relay all of the info about plane identity, route, load and destination, fuel estimate would be computed externally and then be sent back through text message or voice call, pilot would then do his own check. This is really not something you want to get wrong, having multiple go-arounds or a late abort to an alternate for whatever reason should never result in a low fuel condition.
Obviously planes already leaving the gates are fueled up so that's most likely not the case here but that's one example of how those systems can be still integrated. Now, today - with far more computing power - it is very well possible that that whole system runs on the plane side, but the amount of external data and various exceptions and almanac information that was pulled in for those computations was pretty impressive. Most likely that sort of thing is now done on an iPad or something similar.
You're right -- that's what I was trying to say. There are all sorts of external systems tied into flight planning and operations, but once the plane has left the gate the plane should contain everything important already.
Thus, the only reason to recall a plane that's pushed back already would be to avoid problems that would occur only after it has landed. I would be surprised if the external systems were needed for the flight itself.
The 777 has automated presentation of some relevant electronic checklists but these definitely are NOT automated because the whole point is human-attended verification.