the time signal is not built into network antennas: you have to use the NTP protocol in order to retrieve the time on a ntp server. there are plenty of ntp clients, available as standalone executables or libraries.
the gps signal does indeed include a precise time signal, which is available with any "fix".
however, if nor the network, nor the gps are available, your only choice is to resort on the time of the phone... your best solution would be to use a system wide setting to synchronize automatically the phone time to the gps or ntp time, then always use the time of the phone.
note that the phone time, if synchronized regularly, should not differ much from the gps or ntp time. also note that forcing a user to synchronize its time may be intrusive, you 'd better ask your user if he accepts synchronizing. at last, are you sure you absolutely need a time that precise ?