If you have a website, you are at least in the marketing business; rather, your website is a marketing tool, for good or bad. If your website has any features other than basic marketing (prices, times, list of products or services, location, etc), such as purchases, mailing lists, and other such things, then the product you are giving your customers is software. That is in addition to whatever your core business is about.
Someone mentioned a dentist. If his website includes anything interactive, then part of his product to you is software. It might be a stretch to say he is in the "software business", but he (or an employee or contractor) is definitely delivering a software product.
Peter Drucker in "Management: Tasks, Responsibilities, and Pratices" offers the following definition of business and its' key functions:
"Because the purpose of business is to create and keep a customer, the business enterprise has two--and only two--basic functions: marketing and innovation. Marketing and innovation produce results; all the rest are costs. Marketing is the distinguishing, unique function of the business."
If you accept his logic, which I do, then to be in business is to be in the marketing and innovation business.
Using a service does not mean you are "in" that business, any more then being in a shop does not mean you own that shop.
Marketers are in the marketing business. Programmers are in the programming business. Having a website that you use as a marketing tool doesn't make you a marketer, it means you use a product for marketing.
That is just shifting the blame. If you use a product for marketing, you are marketing. Yes, in general, "using a service" does not mean you are in that business. But if you ask your users to take part in this service or tool you are using, you are now providing that service.
Chairs in your office for your customers? You have taken on the responsibilities of being a host.
We can debate indirect services, such as electricity to run a website, and I would say that that line of discussion is pointless. I rely on my electric company, but my customers rely on my website, and the customers blame me, not the provider I chose to host this feature, not the electric company that provides power to the web services provider.
Remember that the customer does not care about your problems. They care about theirs, and they see you as their cause.
Someone mentioned a dentist. If his website includes anything interactive, then part of his product to you is software. It might be a stretch to say he is in the "software business", but he (or an employee or contractor) is definitely delivering a software product.