just watched it.. the video did not show how the software gets connected to the phone. I have emailed them about it since unless they can "push" the software to the phone over the air un-requested by the phone, then you would need physical access to the phone itself.
Most of the information I have seen require physical access to the target phone because the app has to be installed, and the target configured to recognize specific accessing caller ID's. I have seen information that the monitoring is actually done via Internet data packaging (think voip) and the SMS is copied from the SIM immediately after sending, so even if they delete it after, the damage is done. In theory, if this is true, a hobby burner phone with no data plan would be safe except for texting. Also, the apps tend to be only for the major phone operating systems. So the non-smart phones that might be running on Samsung, LG, Sony, etc operating systems probably don't have apps available to be installed.