That was true but nowdays many states, not all, have Buyer's Brokers in addition to the traditional Seller's Brokers. Also, some states have Dual Brokers to handle situations such as a large brokerage house that is both buying and selling houses. And still worse, there are Neutral Brokers in some states. Call your state Division of Registration for Real Estate and ask!
Very often a "Buyer's Broker" is just another name for the buyer's attorney. All buyers should employ technical advisers such as home inspectors, title researchers, surveyors, etc. In some states Appraisal is a licensed profession so be certain your inspector has a license. Check the Yellow Pages.
You bank may want some inspections. But always remember these are to protect the bank's interest, not necessarily yours.