It's six of one and half a dozen of the over. Liverpool City Council told Everton that their plans for Bellefield would be rejected before they applied for planning permission because they didn't meet set criteria. Everton applied anyway on the advice of Savills. The plans were rejected, Everton were advised to appeal against the council's decision by Savills, they did so and it went to a public inquiry. it was rejected again, but not by Liverpool City Council but the Government's Planning Inspectorate (i.e. it wasn't just Liverpool City Council who thought they were unsuitable).
Also Everton were offered the King's Dock around the same time as Liverpool were offered Stanley Park (King's Dock in my opinion was a better deal - Everton had to raise £30m for a 55,000 arena on the Mersey riverfront, Liverpool have had to pay £14m to improve the Anfield area before they can be build anything). My understanding is that Liverpool FC told Liverpool City Council they would leave Liverpool if they did not get Stanley Park.
Liverpool City Council have offered other sites for a stadium (including a bigger footprint at Goodison Park) although the club are still focusing on moving to Kirkby - too much money has been spent on the project to pull out now and contractual clauses would see Everton financially penalised if they decided to pull out. Knowsley Council have built up a bill of more than £3m in legal fees alone. That's not to say that Everton feel Kirkby is not viable, they obviously do, otherwise they wouldn't pursue it in the first place.
More recently..Grosvenor were not happy with the Everton shop in Liverpool One being called 'Everton Two' and be in such a close proximity to the LFC store - were fearful that it could cause fan's to vandalise the opposing teams' club store. It was Liverpool City Council (a man called Nigel Lee I believe) who convinced them otherwise.