On the APA's method for anonymizing papers for review

I'm not sure that the APA has this right.

The APA guidelines for submitting papers state:

All papers are anonymously reviewed. Author's name, institution, or references pertaining to the identity of the author must be removed from the paper, abstract, notes, and bibliography. Papers containing such identifying references may be rejected.

There are at least two ways that one might remove one's identity:

1. One might leave in the references to oneself, but refer to oneself in the third person, e.g., "As Millstein (2009) argues, populations are individuals."
2. One might delete all references to oneself, e.g., "As I have argued elsewhere (reference deleted), populations are individuals."

As I understand the APA instructions and the clarification I received when I asked, we are being told to anonymize the second way rather than the first. However, it seems to me that the first way is superior to the second. If the referee is familiar with Millstein's argument that populations are individuals and the second methd is used, then she will know immediately that the author of the paper is Millstein. However, with the first method, she won't know if the author is someone who is endorsing Millstein (2009) or if the author is Millstein herself. So, I think that the first way does a better job of anonymizing than the second way.

Or am I missing something here?