Normally, I advocate absolute rigidity, but in the case of parting tools, a little flexibility could be an advantage, in that it will allow the tool to "give" when the going gets tough, and avoid a dig in.
The holder that I was given, many years ago, is slotted, and when being used in the rear toolpost, it can be seen to yielding slightly. At the risk of asking for problems, dig ins are almost unknown.
Howard