First, we know for sure SS owned a Samsung Galaxy SIII, as it's clearly seen hanging out of her pocket in some of her NY photographs.
Second Turkish phone makes sense based on the analysis of these variables:
a) Was her Galaxy SIII compatible with Turkish mobile networks? If yes, then she could have used roaming by default. Again, if yes, she could have even obtained a prepaid Turkish line, hooked it up to the phone and used it that way. If no, then a second phone is a must.
b) Even with a compatible device, do operators and mobile network regulations in Turkey allow using any phone you may have brought from abroad for extended durations of time? Answer is no. Any foreign device, not successfuly registered on the central registery will be blacklisted 3-4 weeks after the initial moment of connection to any Turkish mobile network.
c) SS and family's financial status. We know that they weren't exactly very well off. This is important, as roaming in Turkey is extremely cost prohibitive, which makes obtaining a Turkish prepaid SIM card and using it with either your primary cell phone, or even with a secondary cheap cell phone you can obtain from Turkey.
Now, let's go back to SS primary cell phone that we know she had for sure. It's a Samsung Galaxy SIII, and it has many variants. They all look the same from the outside, but hardware is completely different to maintain compatibility with different mobile network standards.
SS may have obtained her Galaxy SIII in US from either T-Mobile, AT&T, Cricket Wireless, U.S. Cellular, MetroPCS, Verizon or Sprint.
If SS got it from Sprint, Verizon, Cricket Wireless, U.S. Cellular, or MetroPCS, her Galaxy SIII wouldn't work in Turkey at all except for the ability to make connections to wi-fi hotspots, as all those US networks are based on CDMA technology. In Turkey, there aren't any CDMA networks, only GSM.
If SS got it from AT&T or T-Mobile, then her Galaxy SIII would work in Turkey, either with roaming or by obtaining a Turkish SIM card. However, as there's a central device registry in Turkey, she would only be able to use her device up to 3-4 weeks. Besides, she would have needed to have her Galaxy SIII unlocked to other operators in the US, as AT&T and T-Mobile lock the phones up they subsidize the cost of. I've already said roaming is cost prohibitive.
So, a second cheap Turkish phone with a prepaid Turkish line makes absolute sense. It would have allowed her to make calls to Turkish numbers cheaply. Also, it would be cheaper for her to contact US numbers through the same Turkish line, as there'd be no roaming involved.
Now, I don't take any press report that doesn't recite a credible GOV or LE source seriously. So, I don't care what the press wrote about a second phone.
But she would have a second phone for all the reasons mentioned above. Any informed traveller on a budget would.