Fumi didn't know Shinobu broke up with Sakura till they met again in talk with the producer. Should you contact a guy who you know he stays with his wife or girlfriend? For what? For Infidelity?
The bad writing is, the author let Fumi be quiet and do nothing though she's the reason of misunderstanding.
In common sense, if you realize you’re the cause of a misunderstanding, you’d try to explain, right?
Imagine you're Fumi. Wouldn’t you try to contact Sakura to clear things up? Why did nothing till being informed they broke up because of you?
Fumi does have Sakura’s phone number. She asked her about gravure work. Could she really just let the misunderstanding persist without doing anything? This is what I call bad writing.
The other just want to separate Shinobu and Sakura by very poor script.