Just as the title asks, if a website needs fixing on the backend, CSS, changes to meta tags, sitemap creation, etc., adding stat codes, meta for Webmaster tools, is this the job of the person hired to do SEO or the developer's?
I would say most would provide that service, but I've seen a few SEO quotes where the SEO company "suggests" changes to your site to avoid having to learn your CMS and save themselves time. It gets a bit out of hand sometimes when your dealing with access issues/working with another programmers code, so many prefer not to unless the job is big enough to justify it. An SEO professional should have a good understanding of CSS/HTML. One that doesn't have these skills can't be very good IMO.