Illegal in airlines. The RIM and other two-way pagers are "intentional
radiation" devices and are not permitted. [Cell phones also fall into
that category, and the plans for eventually allowing them include
"fake" cell towers to force them to minimize radiated power.

What you saw on the referenced web site uses a different system
(PalmNet) which is permitted (mostly because it is not specifically
illegal G) and is aimed at General Aviation. There are two issues:
FCC and FAA. The FCC blocks the older-style cell phone protocol from
airborne service. [The newer style simply won't work.] The FAA blocks
these RF Radiation devices from airlines (currently), but they are
permitted on a pilot-approved case-by-case basis for GA.

BTW, PalmNet was shut down last year and is no longer in service. A
lot of pilots used it for just what you mentioned, but it couldn't
compete with the commercial cell phone industry for terrestrial
service.