In a word, no. Any competent programmer can build the content management system and associated functionality for your site. PSD to Final uses common open source platforms that are well known, well supported and work on more than 95% of website hosts.
It is important to remember that not all IT is the same. People often specialise. While your IT support company may be very good at hardware and servers, they may not specialise in website development. When deciding who you would like to build the “back end” of your website, ask yourself if websites are the core business of the company you are considering, or if it is marketed as an additional service.
We always recommend you use a specialist company for your website needs rather than a “jack of all trades”.