Yup, and running your own server instead of leasing a server, you're talking big bucks, not for the server but for the line from the TeleCo itself.
When I used to work security at my last workplace, the various businesses would run their own servers and lease their internet connection from the TeleCo's. Anywhere from DSL for the really small businesses to several T-1s for the larger Businesses.
Every so often I would have to escort a service guy from one of the TeleCo's to the Server room from one of the Businesses so they could switch their lines to a different TeleCo, just to get a cheaper price. This is something that goes on all the time and if I recall correctly from what one of the service guys told me, companies generally bid on pricing contracts for the lines which is why they are constantly changing service all the time.
So unless you have a business that is doing well and has the financial backing, you are probably better off leasing a server unless you can get a good deal on internet service line contract.
But this option will cost you as there is a major investment in TeleCo equipment, servers, business class routers, Server Rack, Rack mount UPS, Hardware Security Device and what ever other hardware may be needed to setup.
Although once it's paid for, it's yours scott free until you need to upgrade to something newer which will mean even more investment.
Almost forgot to add, the ones using DSL, didn't have their own servers as they leased them from a hosting service instead.