You are mostly correct. Except there's LG logo on back. The phone itself is unlocked but I have learned that some carrier further use it's hardware like T-mobile. The original nexus 4 I brought from Google doesn't have 4G out of box but rooting and flashing radio will open up what Google and LG had blocked.
Touch?..... I should have been clearer on the logo. Yes, there's a small LG logo on the back. I meant when you turn on the phone there is no manufacturer's/carrier's logo or pop-up- strictly Google.
About unlocking radio bands and rooting that's a whole other subject. Carrier locks was the concern- to be able to use a Dominican wireless service.
P.S. opening/unlocking your 4G aka LTE radio on your phone did no good in DR. The one or two Dominican wireless carriers that have deployed LTE (4G) do not use any of the bands the Nexus have. This is a
hardware limitation.
List of LTE networks - Wikipedia, the free encyclopedia
P.S. There is also two versions of Nexus phones; European and North American. Both with different
hardware. The European model will
never work on North America's 4g (LTE) networks and vice versa. They, however, are international "Quad" phones and will work on the extremely slower GSM networks, meaning you can use voice but no data (internet).
The best way to tell if your phone is
carrier locked is to insert a foreign SIM into your phone, it pops up a requester for an unlock code or it states "invalid SIM" it's carrier locked.