I agree in general, but easy fizzbuzz-type questions are not the main problem with interviewing process by far. There are just too many people who almost cannot write code, including CS PhDs.
This is true. For CS PhDs you should always look to see if they've done any large implementation work or if they've focused more on math. The former will generally have large amounts of source code available for inspection. The latter may or may not be good at programming.
