Absolutely. The Real Estate company will typically have you sign a piece of paper known as an "Affiliated Business Arrangement". This document will explain, in this case, that it is customary to get a home inspection when purchasing a home, and that they have an interest (whole or part ownership) in an inspection company. It will also state that while they may recommend that company, you are under no obligation to get a home inspection from them.

These documents are fairly standard in a number of business, including most anything Real Estate related. Because there are certain synergies between business involved in Real Estate, companies will often purchase or start up a firm to allow for "one stop shopping". You will often find relationships between lenders, Real Estate companies, title or escrow companies, insurance agencies, home inspectors, etc. The important thing to note is that, while these companies are required to inform you of their mutual interest, you are under no requirement to use their affiliated company. Often times consumers should shop the affiliated company on their price and service with their competitors to make sure they are getting a fair deal. There is nothing wrong, or under-handed about Affiliated Business Arrangement's as long as they are properly disclosed, and you are given equal right to obtain your product or service from the company or individual you choose.

If for some reason you were not given an Affiliated Business Arrangement, or not given the opportunity to choose the service provider for yourself, I would question the person you were doing business with on why. It is illegal for any individual or company to require you to use a certain service in a Real Estate transaction.

The whole purpose of having a home inspection is to have someone with no vested interest in the transaction inspect the property.  You can always insert a clause in the contract offer that the home inspector must be someone of your own choosing, but that would seem to be redundant.  You should not have to put in such a clause.  The home inspector is supposed to represent YOUR interests.  If a Realtor owned inspection company is doing an inspection, then your interests are NOT being represented.  If a real estate office balks at your insistence on having an independent home inspector perform that function, then you should probably re-think as to whether or not you should be doing business with them.