He's probably right in that the American culture / schooling seems to favor memorization, but the distinction between "problem solving" and doing things by recall is fuzzier than he implies. A lot of problem solving can be cast as examining details to find a match and looking up how to proceed. (That's not a terrible description of Prolog, come to think of it.) The reverse is true, as well.

Is a sysadmin troubleshooting an erratic network and starting with checking DNS doing what he calls problem solving ("my experience says checking this will narrow down several potential causes") or working off memorization ("many cross-cutting issues are caused by DNS, check there first")?