One affects the other. Out of universe Snyder could have replaced them or used many of them, he did neither - leaving Superman without his traditional allies or supporting cast. It's not about Clark trusting the general, it's about him as Superman having a relationship with him and he hasn't got one in either identity.
In universe Superman is alone, all he has is Martha and Lois, until Batman arrived and he spent most of that time trying to intimidate or kill him. The fact they didn't exist in the DCEU are a choice Snyder made, he didn't want them doing anything. Perry's role is reduced, despite the fact he set up a good piece for a conversation about how the two feel about Batman in it.
Wonder Woman is in the same place in B v S, she has nobody until she teams up with Batman. She has got get her solo movie before she gets any of her traditional allies to support her. The ones she does mention in B vs S are long dead.
None of these people are the "lone wolves" Snyder makes them out to be in his control because those aren't stories he wants to tell with them.
Even in Nolan's Bat films he had many allies in it, he just focused on the non-costumed variety aside from Catwoman. Snyder just reduced Batman to Alfred, killed a Robin and everyone else is not worth a mention.
They are when Lex becomes more like Joker than how he's supposed to be written. The jar thing is a joke Joker himself would love to do. Those "quirks" inform his character to his detriment. He's meant to be Zuckerberg instead he's Joker 2.0.