Nope...

Eligibility Rules

The eligibility rules to play in the AFL are simple.

The roster size is 30 players per team.

Each Major League organization is required to provide six players subject to the following requirements:

All Triple-A and Double-A players are eligible, provided the players are on at least a Double-A level roster no later than Aug. 1.

One player below the Double-A level is allowed per Major League team.

One foreign player is allowed, as long as the player does not reside in a country that participates in winter ball, as part of the Caribbean Confederation or the Australian winter league.

No players with more than one year of credited Major League service as of August 31 are eligible, except a team may select one player picked in the most recently concluded Major League Rule 5 Draft.

To be eligible, players on Minor League disabled lists must be activated at least 45 days before the conclusion of their respective seasons.

I may be mis-reading something, in case I'm not, then your sources are incorrect.

AFL eligibility states a player must be on a Double A roster by August first.

Each ML franchise can select one player below Double A to participate, so "selecting someone else from A ball" wouldn't be allowed.

All players, regardless of classification, must not be on their respective team/league disabled list no less than 45 days prior to the end of the regular season.

Based on that, Jeffress may be inelgible on two points. I don't know when he was activated from the DL, and he wasn't on the Double A roster on August first. Pretty cut and dry he's not coming.