I know it seems kind of convoluted, but I only see 2 things as vital -- look like you know more than you do, and support that appearance for others. And look like you are loyal to each other, even if you aren't always.
Bill looked quite smug when Ice asked who would contact him. Then, you have him (and Z, and IM) unaware that one of their own in their midst was reporting back to BB. (Presume she wasn't reporting on them, of course.) She'd never even introduced herself as working for anyone, or shared any info that she HAD gathered. She came in, and left, and gave them nothing, and then he found out she was probably giving all her info to BB instead.
Then you think she probably knew he was asking BB for work, right? And if you assume she did know what Ice had done (for Alaska, for Madeline), she would know what he was capable of. She never consulted him about passing any of that along.
Both of those things -- making him look oblivious to a boggan, not getting any help or info from him -- just seems to ME, like it would have been a faux pas on a few levels. Disagree?