I cannot access the paper, but in the introduction it also says that only 40% of new members are women.
The most likely conclusion is probably a convex combination of
1. Most of the time it is quite clear who is the best candidate and no gender-based tie-breaker is required
2. Publication- and citation records (which anyway are a lousy measure for scientific merit) are very heavily gender-biased (this was asserted in another comment)
3. The AAAS and the NAS use saner criteria than those publication- and citation records.
My guess would be that 3. has the highest weight of these.
1. Most of the time it is quite clear who is the best candidate and no gender-based tie-breaker is required
2. Publication- and citation records (which anyway are a lousy measure for scientific merit) are very heavily gender-biased (this was asserted in another comment)
3. The AAAS and the NAS use saner criteria than those publication- and citation records.
My guess would be that 3. has the highest weight of these.