It depends on what you mean by "change your business." A web host can affect your business and how you do business in several ways. In some cases, they may actually require you to operate your business in a certain way.
Affecting How You Do Business
A web host may affect how you do business due to the technology they have available for you. So you may have to tailor your internal company practices to conform with the technology your web host has.
For example, if your web host only supports PHP and you want to bring in an ASP .NET programmer, you are either going to have to give up on the idea of ASP .NET or you will need to change web hosts.
Requiring that You Do Business a Certain Way
All reputable web hosts have a Terms of Service (TOS) or its equivalent. These are basically the rules you have to abide by to use their web hosting service.
If your business is doing something or plans on doing something that violates or will violate the TOS, they can and will demand that you change your business practices and not violate their TOS. If you do not comply, they will typically terminate your account and not give you a refund.
For example, a web host may require that you use double opt in mailing lists. If it was a business practice to collect emails some other way (perhaps via business cards or some database you have), they may require that you to change your business practices so that all recipients of your mailing list are double opted in.
In some cases, the web hosts may simply be enforcing the law, by requiring you to operate your business in a certain way.
For example, the CAN SPAN ACT requires businesses to send their commercial emails in a certain way (a real from address, relevant subject lines, a legitimate physical address of the publisher and/or advertiser is present, etc.).
Affecting Your Revenue or Reputation
If the web host goes down, goes out of business, is hacked, or something else bad happens, it can have a negative affect on your business. You can lose customers, valuable data and revenue. It can also potentially harm your reputation.
For example, if your web host goes out of business or your server is down for a week, you lose all the revenue that came from your website during that time period. If you do not have your own backups, you may also have lost valuable data that you either have to spend time rebuilding, or is simply lost forever. If you have an online business where you offer a web based service, your reputation as a reliable provider would be tarnished.
As you can see, your choice of web host can affect your business in many ways. If you don't like how a web host is affecting your business, you can always move to another web host that has different rules.