If this is true then Gibson will sack him immediately, remember Garry Monk and the Swansea situation Monk breached his contract by getting his agent to sound out Swansea on a possible return, football is a village and I can guarantee that at 90% of managerial changes, particularly mid-season are done deals, if Bournemouth wanted Wilder they'd have made an approach via a 3rd party, if Wilder has been doing a Monk then he'll go, Swansea weren't interested in having him back but he continued to try any push it.
As for Mowbray, he knows a mate of mine very well and has never said anything negative to him about Wilder, in fact quite the opposite nothing but praise for him as a manager and a person, he wasn't so complimentary about a previous incumbent in the role.
Wilder needs to improve results and fast, he's had one bad season at a club in 20 years of management which for me, a track record like that, should buy him a little bit of time, from what I've seen of us this season we're in a false position, too many missed chances and defensive errors are undoing decent spells of controlled play.
The results will come, or he will go, October is an important month and if Wilder is ambitious then he needs to work on fixing the problems that have become apparent over the opening weeks of the season, settled defence, more energy in midfield and better conversion rates from the strikers.