Closet Index Fund - Portfolio Management

I keep stumbling on the same mistake.

Holt is least likely to be correct about which factor as an indicator of a closet index fund?
A. Low active risk.
B. Low information ratio.
C. Same Sharpe ratio as the benchmark.

The answer was B. However, I chose A because the way I interpreted it was that for a closet index fund which they claim to be actively managed ( even though they are more passive), they must take a lot of active risks, which consequently lowers their information ratio because they are not able to beat the benchmark.

The answer said that because they are passively managed their information ratio is 0 which I get, but wouldn’t my point be valid as well? Let’s say they underperform their benchmark. In that case, their IR wouldn’t be 0. It would be just low.