The main responsibility for the problems of the Jamestown settlement had to do with the way the colony was imagined, not with the way that it was run once it was set up in Virginia. Therefore, the fault is more with the company directors.
The company directors assumed that the settlers would be able to find a labor force among the natives. They expected to make money by trading with those natives, using them as workers to produce goods, and by extracting precious metals from the earth. None of these things turned out to be possible. The colony suffered mainly because of this. The strong leadership of John Smith (though he had flaws) was what kept the settlement together until a different economic model could be devised.