Brief vibration in reverse

Hi there,
I am looking to buy this very well-kept truck. It has been cared for meticulously and has low mileage for the year at 85,000. The truck has been very reliable. The owner mentioned that the only odd thing is that when you first start it up if you go directly into reverse, it will vibrate or "hum" as it moves backwards. Once you go forward a few feet the vibrating goes away and does not come back even when in reverse again. This only happens when you first start up, and only if you go into reverse directly.
The owner said that the transmission was replaced early on at 30,000. It is an automatic, 4x4.
Any ideas on this? I am going to bring it to a shop before buying it, but I would like your two cents worth.
Thanks