The questionnaire option is clearly one that BRCGS does not like. If you look at the interpretation guideline there are several caveats around this clause such as:
"The auditor will expect to see, and will challenge, risk assessments"
It also recommends reviewing the risk assessment on any change. So for example, you do a risk assessment and the supplier origin of one of the ingredients in the supplier material changes. Could the auditor then argue that if there is a risk with that ingredient you should have reviewed your risk assessment.... etc.
Across the world, legislation for food industry differs WILDLY. I went to a UK producer (non GFSI) the other day who I am surprised are still trading. I'd say for food ingredients, I'd really wonder why someone doesn't want to go for a GFSI standard unless, perhaps for packaging. I'd wonder even more why our procurement team are insisting on it. And yep I'd be going to visit that team.
While the previous poster is right you don't have to test their trace as part of a questionnaire and you don't have to audit, considering this company doesn't have GFSI and not all legal requirements go as far as GFSI does, I would struggle to see how effective saying "do you have incoming and outgoing traceability?" is as a question without testing it.