Under 91 you certainly can, however I don't think that is the jest of the question.
Under 135 and 121 you can continue your approach if inside the Final Approach Fix (FAF). However, if you're outside the FAF you can not accept the approach clearance, because 4000RVR is less than 1 1/2 miles. There are some conversion tables in the front of the Jepp and in the AIM that clarify this issue.
These tables basically state what visibility you can use if RVR is not available, but it only stands to reason that you can also do the reverse if sm is not available.
I would imagine this question is more directed towards your general aviation knowledge than the specifics of RVR vs. vis. The interviewer was probably just seeing if you knew that at 4000 RVR you're probably not going to see the runway if the approach requires 1 1/2sm.