Everett didn't make anything difficult for Bristow. My understanding is that Bristow didn't have the preferred aircraft type available, simple as that.
??? Bristow provided the aircraft type requested in the original Statoil contract - the AW139. As has been mentioned already, Statoil terminated the contract in 2015 due to the falling oil price that made exploration unprofitable.
Everett had some excellent people at that time but a disfunctional individual at the top of the food chain made life difficult. Everett had established a business in East Africa that was very competent at bush flying operations. That does not necessarily translate to providing an EASA standard, deep water, daily, offshore operation with suitably qualified and experienced offshore flying and engineering crews supported by a LIMSAR operation with qualified and experience SAR crews that was acceptable to Statoil.
Because of this and local political sensibilities the Everett/Bristow arrangement was established.