IMHO, it means that a particular small literary zine does not want first person accounts within its particular small literary market niche.
Your results may differ.
That is, other zines likely differ, and on different variables at that.

After writing the first five volumes of my series in third person, the sixth is structuring itself in the first person among four different POVs. I have to work harder in first person than I had in third, because I must get more deeply into the characters' heads and become more familiar with their internal languages and voices. Writing in third person, I used an ovearching narrative style within which I could "visit" my POV characters, but in the first person that style no longer applies. I can't visit them, I have to "live" inside them instead. That's led me to do more rewriting and tweaking because it involves an extra layer of translation and intimacy. Hardly "lazy" if you ask me.

Magazine specs get funnier and funnier. I've had to change the marketing handout I use in my course several times over the years, and what saves my butt is that I tell my students first and foremost to check the specs for each and every market, and to revisit those specs because they change over time. Used to be one submitted queries for novels or nonfiction articles but not for short fiction. This year I've had to submit queries to two short fiction markets before getting greenlighted to submit stories. And on one of those, in addition to getting greenlighted, I was told to submit my story in 14-point Arial, single spaced.

When I saw that e-mail I went: Say what?

So I did a Save As, re-titled my file, reformatted it according to those specs, and sent it off. All those "rules" that say to avoid sans-serif fonts, use only monospaced fonts, double-space manuscripts, and stick to 12-point type go out the window for this particular market, though those rules are still considered the "standard."

If one zine doesn't like first person narratives, that's the prerogative of one zine, so far as I know. Publications can be fussy.

"Accounts" is the word that strikes me funny. It almost sounds amateurish. I wonder if this particular small literary zine gets submissions that are not really fiction, but rather personal experiences that the writer thinks qualify as a "story," and will be acceptable because the magazine is "small."