It's the producer that gets the credit for a Best Picture Oscar, not the director.
The producer of Rebecca was David O. Selznick.
Alfred Hitchcock was nominated for the Best Director award five times (including in 1941 for Rebecca), but he famously never won it. His only Academy Award was the Irving G. Thalberg Memorial Award, which is awarded periodically at the Governors Awards ceremonies to "Creative producers, whose bodies of work reflect a consistently high quality of motion picture production". According to Wikipedia, this counts as an "Honorary Oscar"; Hitchcock won it in 1967.
Rebecca is the only recipient of the Best Picture Oscar since 1936 (when awards for actors in supporting roles were first introduced) that didn't win any for acting, directing or writing.
If you want to test contestants' knowledge of this subject, the question might be better worded "Which film directed by Alfred Hitchcock won an Oscar for Best Picture?". You might even preface this with "Although he himself never won a competitive Oscar, ... "
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