Ah, gotcha. For me, all actions she does on Lovers is cheating no matter how you look at it, forced or willing. E.g., when she 'willingly' comes to Matt because of the vibrator, she already cheated by intention, doesn't matter if the MC then prevents or not that under-desk bj. She could just masturbate in the toilet and not go give a blowjob to Matt, whom she hates on Lovers, on her own initiative.
So my own explanation is that on Happy/NTR the cheating counter is simply a statistical number, while on Lovers it's an important game mechanic that allows players to stay on Lovers or fall off to Happy/NTR in future developments. So dividing those blowjobs into cheating and non-cheating simply serves the purposes of that mechanic, no need for us to overthink the logic of it. This bj is 'forced' and that bj is 'cheating' just because the dev decided that way

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