She's her own person and can get agreement with F to sleep with other guys in a swinging manner out of respect for being open+honest with each other, but he's not her pimp and she makes her own decisions. Likewise if F wanted to swing with her knowledge.
NTR is cheating and/or being unfaithful, even though it's more complex than that before translating from Japanese:
You must be registered to see the links
Regardless of the complexity involved, NTR isn't about accepted swinging with others, nor is it an open relationship that still maintains the core partners without deceit.
There is a hidden or unfaithful aspect to NTR which is not what DMD is proposing to offer and the presence of someone in a room or not doesn't change the aspect of it being an openly admitted sharing of sexual activities with others ... with no attempt to hide that activity or be unfaithful to the other partner in the process.
Some modern-day subcultures are fixated on cuckoldry as an insult and have abused the terminology to include all sorts of things in the most negative fashion possible. NTR has been thrown under that umbrella at times and this is a problem for those who see that terminology as failing us due to misuse.