I work for a quickly growing startup and this reason given is a lot more clear than I expected. I’d believe them. Not everyone does well with little direction. In fact, most don’t do well. They’re probably looking for someone that is highly motivated, can learn quickly on their own, and make decisions and take action with little to no direction.
For our in house IT team (which is like 4 people in a company of 200 separate companies to support), all of them have been head hunted from other large companies and have a proven track record of growing their own teams. They’ve all been leaders (director, etc) in previous jobs.
Also, with a small team fit is probably the biggest thing they’re looking for. If they don’t have confidence you’d clic with the other members then they won’t go forward.