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I say this is total and complete rubbish.
The sitemaps feature in Webmaster Tools was created as a way to help sites identify all their pages to search engines and let search engines know when they add or modify content. They also enable search engines to flag errors in reaching specific pages. They have nothing to do with ranking - they merely serve to help with indexing, if your site needs a little help.
Where a website has been built correctly so that all its pages can be easily found and crawled by search engines, then an XML sitemap is not strictly necessary. In fact, any good SEO firm should be able to ensure through good coding and well-designed information architecture that no client's website actually NEEDS an XML sitemap in order to get its pages indexed.
Why (and when) you should still use XML sitemaps
Just because an XML sitemap should be unnecessary for your site does not mean that having one isn't best practice for SEO.
First, creating one is easy - there's a lot of places that will generate one if you don't have an XML feed setup, and you can quickly generate and upload a new one each time you update your site. If you want to avoid having to do this regularly, however, setting up an automated XML feed that updates itself everytime you update a page then your SEO company should have the skillset to get this done for you (or, if you have a separate developer, your SEO company should be able to advise them on how to do it). Normally, if your site has been built correctly, it shouldn't really take all that long.
Second, should something go wrong - should you find pages are not being indexed - having an XML sitemap may enable you to find out quickly which pages are the problem and why the problem exists by looking at Webmaster Tools.
Third, it does flag up to search engines the URL of every page of your site. This is useful particularly for large sites that have pages 4, 5, 6 or more levels deep as it may speed up the process of your deep content getting found. This is not to say it will speed up the crawling and indexing - but it may help, so why not try it and see.
Finally, if you update your site daily, or several times a day, then having an automated XML sitemap can help search engines understand that they need to visit your website more frequently in order to ensure they have the most up-to-date information.
So, yes, your SEO company should recommend an XML sitemap for you - at some point. However, if it's a question of what work to do
first, if your pages are being found and there are other things that will deliver results more quickly, then don't worry if they wait because not having one won't harm you - and if they're doing everything else right, having one shouldn't make a difference.