>"Planefag, is this normal? It seems odd to me that a NATO plane is circling around the southern US with no destination."
Not a planefag, but logged lots of hours in that area
Pure speculation:
Could have diverted into US airspace due to weather/aircraft malfunction/etc.
If diverting, USADIZ (US Air Defense IDEN Zone) would probably have given them "vectors" to keep away from critical areas while they ran the background check on the flight.
If penetrating ADIZ without talking to ATC, they call you on Guard Frequency with "Unknown Rider, Unknown Rider, this is Sierra Pete on Guard…" then tell you where to go and what to do [I have had a little experience with this].
https://www.faasafety.gov/files/gslac/library/documents/2011/Jan/49877/ADIZ%20TFR%20Intercepts%20w%20answers.pdf