I'm a developer / seo from Australia and we've found this is correct.
A lot of cheaper hosting companies are obviously in the US and even though they're cheap we've been progressively moving over clients to our servers here for better results. I haven't tested it thoroughly, but I would think even moving a specific site to it's closest location would effect SERP results. Meaning if you were looking for dry cleaning in Washington, you might find it helpful to get a Washington based hosting company. Then, when google crawls your site, it will find the information on a nearby server and this might even make the site slightly faster in terms of response times for requests and this would effect results (even only minutely).
Having said that, like everything in SEO it's just one of the hundreds of factors involved. Moving your site nearby won't fix everything automatically...but it's something that can be easily changed for a relatively small fee.
