Yes, the U.S. FCC agency makes Verizon sell all LTE phones now unlocked to work with any carrier, as long as the LTE bands are compatible.
This was part of the agreement for Verizon to get more LTE spectrum from the government.
AT&T did not have to make this agreement, only Verizon.
The issue is for most people living in other countries (most, not all), they don't need CDMA but they do need HSPA and LTE.
The XT1225 "international" Moto Maxx/Moto Turbo has more HSPA bands and more LTE bands AND has easily unlockable bootloader. But a lot of people only know about one Quark -- the Droid Turbo, when there are better versions out there for their purposes. The Verizon public relations machine LIED and made people think the Droid Turbo was "exclusive" WORLDWIDE, when it wasn't even exclusive in the U.S (Many regions CDMA/LTE carriers in the U.S. sold identical phone!)
So, people don't know about the U.S. Moto Maxx (XT1250) which is identical in every way to the Droid Turbo (same radio bands, same FCC ID) or they don't know about the XT1225 "international" Moto Maxx, which has more HSPA and LTE bands (but not CDMA bands).
Basically the Moto "Quark" is like a an LG G4. I'm using that premium LG phone as an example. An LG G4 has the the same hardware, no matter where sold, no matter what carrier -- but has different radio bands (and different model number) depending on the region/carrier. But it's
STILL an LG G4 -- whether sold in Europe, India, South America, or by Verizon or AT&T in the U.S.
Basically that describes a Moto Quark.
Verizon's Quark was called the Droid Turbo. That's all, it's still just a Quark. The only thing "exclusive" about it was the locked down bootloader.

Motorola gave the same phone to other carriers, the same way LG have the G4 to other carriers besides Verizon. Other Quarks are called
Moto Maxx or
Moto Turbo, but you have to go by the MODEL NUMBER to make sure you have the right one, since there were two Moto Maxx models with different radio bands (XT1250, XT1225). Then in India, the XT1225 was re-named the
Moto Turbo, since there was an Indian phone carrier named Max or Maxx, and Motorola didn't want people to think this phone was affiliated with that carrier. So, even the "Turbo" name was not exclusive in any way.
You can't say "I have a Turbo!" There were TWO Quarks called "Turbo". You have to use model names, XT1250, XT1254, XT1225 to differentiate between the Quarks.
(Verizon owns the rights to "Droid" name in the mobile arena, licensed from LucasArts/Disney and can call ANY phone a Droid -- even crappy low end phones, if they wished. "Droid" does not mean anything, and is not limited to any manufacturer. So far, Verizon has only used it with Motorola phones, but Verizon controls the name, not any manufacturer.
Verizon now has mid-tier phones with Droid name, so they are not even pretending Droid is a premium phone any more.)
By naming the same Quark phone by different model names caused a lot of confusion, but Verizon demanded that so they could PRETEND they had some exclusive phone. Same way the
Droid Turbo 2 was the
Moto X Force everywhere else. No exclusives -- just a different model name for Verizon for the same phone.
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See this post for more information about bands. Italy is like France -- you'll get LTE bands 3 and 7, but not LTE band 20. What HSPA bands do you need?
http://forum.xda-developers.com/showpost.php?p=67657958&postcount=3