It's trivial to to tap a phone call on Mobile. There are three methods:
1) A fake mobile Base station does a "man in the middle attack". Favourite by spies and governments, and been done without warrant.
2) A SDR setup and computer. Anyone can do it. If the operator is running 3G AND the best encryption, it might be harder. GSM and CDMA is trivial, as CDMA has no sensible encryption and GSM operators are still using compromised encryption (they can in theory deploy better).
Both these need radio range to EITHER phone.
3) A network attack. This can be covert in the operators central premises, a "back door" in the operators equipment or with secret cooperation from the operator.
Solution?
Use a server with VPN server on the Internet. Both people connect to it in Internet data mode (GSM, 3G or 4G works!). The VPN uses an app on the phone to provide encryption. If done properly even NSA or GCHQ can't decode the data (they can though record it and know how long the connection lasted, which masts both phones used, and what location they connected to on Internet via 1, 2, 3 or even regular suspicion and court order after the fact.).
You then use a low bit rate voice codec over the VPN (specialised VOIP app), or text or both.
I've done this on a laptop from central Europe to my server at home, with VPN cloaked as a website (we did that because the lads in college here found only Web ports open), a smart phone is just the same, the apps are available.
If she buys two pay-as-you-go mobiles in America, they'll only work by a shared network here, right?
1) Many PAYG US phones will only work in Europe if Triband or quad band, as USA uses different bands. USA CDMA phones don't even have a sim and only work on one operator and only in USA.
2) Two US phones that DO work in Europe, that have USA sims, will not actually route the call via USA. Only the meta data will go to home USA operator, the actual call will be routed locally via the Roaming partners. If there is no roaming partner, then you can't call anywhere on your USA phone, even if compatible.
3) You pay extra for a phone not sim locked. There is no advantage on a foreign phone with local anonymous SIMS. Eventually anonymous SIMs will be illegal, you can't get them in Spain and some other countries now.
If you have anonymous sims the unique phone IMEI is still logged by operator. GCHQ or NSA might be interested and investigate closer if the same phone is used repeatedly with different anonymous PAYG SIMs! They automatically get all of that.
Let me know if anything needs clarified. I've worked in Telecom related stuff off and on for a long time.
Even Tor users can be tracked, though that helps. But Mobile Phone Internet uses deliberate deep packet inspection and often proxies on the Edge Routers, so it's very trackable.
Fixed real broadband users of Tor, the GCHQ/NSA etc first has to know who your ISP is. They can figure that if they know where you live.
A call box (if you can find one) and they don't know you are using it is more secure, because while it's trivial to tap (for ANYONE), they have to be following you to know which one you are in. A phone is UNIQUE apart from the SIM and that info along with location, signal level, time and duration is logged, so they only ONCE need to connect your phone IMEI with you for SIM swapping to be pointless.
EDIT
I suspect you can tell from IMEI the make, model, when made and where the phone shipped to. If you are a Government. I can't. Well, I've not looked. Maybe someone has posted a database somewhere.
EDIT 2
Some phones you can edit the IMEI! Of course you need one that's registered somewhere. Called phone cloning. Usually the SIM is cloned too.
I don't think that helps.
In general there is no value in buying anything electronic in USA for use outside USA, either to save money (as it might not be 100% or at all compatible elsewhere, even if made in Turkey / Korea / China) or for covert reasons.