EMSA likes redundancy. Info is sent in numerous ways.
Every crew member has an alphanumeric pager, on a EMSA dedicated frequency, a portable radio- (will each have one when on 800mHz), their own personal cell phones- and a company issued cell phone. There is a MDT(Mobile Data Terminal) in the new ambulances- which displays dispatch/call info, as well as having a mapping feature.
The computer you describe as being seen in the hands of the medic- is what we do our 'paperwork' on. It is a tablet PC that runs a program called MEDUSA Siren. It does have wireless internet, and recieves information from dispatch- but this is after the fact - and for the completion of the paperwork... it does not recieve call info.
EMSA medics recieve call info by voice[radio], pager, and MDT. If there is something that they don't want to say-- or a FUBAR situation we are getting called out to - they will page us/ask us to call dispatch.
Mind you this will all change when 800 mHz radios are issued in December.