Opinion: Accessibility is a website owners responsibility. Is it?

Responsibility and liability are different things. I think the website owner is liable, but should take advice and suggestions from their responsible website designer. 

The law says that it is. However, as experts in their field web professionals will be best placed to advise website owners on this. Accessibility considerations should be at the heart of every project.

Obviously! But a professional web design agency should include such accessibility discussions and practical implementations within their service.

Yes it is. If your website is/was designed by a good webdesign agency then they would have thought about accessibility from the outset.

If not the website owner, then who else? Then again, any website which is well designed and uses modern standards will automatically be accessible.