This is a good example why Home Inspections should become a required part of the Home Buying process.
If you were buying a home, would you allow the listing agent pick and order your appraiser for you? Fortunately, the appraisal is usually a mandatory part of the process when lenders are involved, and any meddling by a Realtor creates a serious conflict of interest, whether real or perceived. If you answered no to the first question then why would you allow the seller to pick the Home Inspector, as a home inspection can have just as much or more of an impact than the appraisal, as I have personally seen several transactions cancel after an inspection where the appraisal came in fine.
In full disclosure, our firm is on the referral lists of several Real Estate Brokerages, and I have personally been referred by listing agents that were acting on the behalf of both sides of the transaction. I also feel strongly that most of my peers that are on the same reference lists would never skew a report for a Realtor. I also feel that most Realtors would not ask a Home Inspector to manipulate the transaction. However, most is not 100%, and it does happen, so you should vet your inspector whether you found them on the internet or referral sheet from a Realtor.