The World Wide Web has its own culture, one in which high pressure and overblown advertising claims are not acceptable. Don't use a Web service that promotes itself like that, and don't let them design you a web site like that. Don't be intimidated by technical talk. Ask a lot of questions, and make sure you understand the answers. Take some time to explore the Web yourself, and see what's out there.
Designers have to take the technical demands of the Web into account.
You'll also see web pages out there that are designed by computer experts with no professional design background, and it shows. Ideally all aspects of web development and design should be performed in-house, not contracted out. These factors work together to produce a single, unified product. To really make a web site work, you will need a server staffed with professionals in the areas of networking, telecommunications, hardware, and software. The Web, as user-friendly as it is, can only function that way because it is undergirded by a solid but complex set of technical specifications in each of these areas.