I'd agree that there are people are against it simply because it's not within the city boundary. Personally.. I'm not too bothered about that, but the backlash would have been more severe had Tesco and Everton chose Birkenhead as a suitable area despite being a similar distance away.
Whether it's a flimsy excuse or not is debatable, the club's local authority has differing importance from person to person. Knowsley Council have said they want to brand Everton as the football club of Knowsley, some will see that as wanting to remove the Liverpool element of the club or bastardising the brand.
Knowsley Council see it as an opportunity to promote the Knowsley brand because people from other parts of the country don't know it exists.
I think Elstone is being mischievous with the "few hundred metres" quote, the distance from the stadium site to the council border is not the problem, it's the distance from the city centre. I've seen people bring up Old Trafford as an example of a team being located in a neighbouring authority but it's only 2 miles from Manchester city centre, Kirkby is around 3 times further away. I know people who are equally opposed to sites in Speke and Croxteth for logistical reasons.