In my experience it is even worse than that. I interviewed several professional statisticians with regard to consultancy on a particular experiment. They all wo

In my experience it is even worse than that. I interviewed several professional statisticians with regard to consultancy on a particular experiment. They all worried about different things (sources of error or misinterpretation), according to what in their career up to that point had been important. It was clear to me that to do the job properly I would have to worry about every thing. And I couldn't trust any of the statisticians to do that well for me, as none of them were aware of all the things. I suspect this is only done well in extremely narrow domains - maybe nuclear physics (e.g. CERN)? Where everyone present is extremely well educated about the statistics - not as a separate discipline, but as necessary background understanding to do non-statistical jobs too.