Let's start by talking about fan-made games, fan works are typically non-commercial or generate minimal profit:
Official companies often turn a blind eye to small-scale copyright infringement initially, as the legal costs outweigh potential gains (fan creators usually work out of passion rather than profit, making them unlikely targets for lawsuits). Moreover, cracking down harshly on fan works could damage community goodwill toward the original IP.
"Appropriate" fan works are usually tolerated—they boost community engagement, extend the original work's lifespan, and may even drive sales of official products through renewed fan enthusiasm...
This unofficial permission is a delicate balance of interests, relying largely on community self-reqgulation. It's more of a one-sided "privilege" . (For OpenBOR games that directly reuse official assets—graphics, audio, or text—companies may abruptly change their stance, leaving creators' efforts in limbo.

)
As for OpenBOR fan games in this legal gray zone:
Nintendo likely wouldn’t openly promote them.

Fully original OpenBOR projects might have virtual cards... maybe?