I wouldn't think any significant form of active transport would be going on in a dead bird. Also, I think the sodium-potassium pump pumps sodium out, not in, although you could be talking about a different pump?
In the absence of any pumps going on, I would imagine a 35% solution would be extremely hypertonic compared to the interior of the cells, and water would definitely flow out.
Do these cell pumps work even when the cell is dead? I was under the impression that ATP was required for that.
As far as I know the definition of osmosis is a movement of solvent across a membrane, without extra energy input, so I don't think "salt osmotes into the cells" makes sense. It would be diffusing along the gradient or undergoing active transport. I'm not a chemist, though.
Let him know in the seriouseats comments... He's a really cool guy and would genuinely like to learn if he's ever incorrect about something.
This was what I thought was happening as well. Even without active transport (because that turkey is dead) some salt should work its way into the tissue, after all it remains salty after a thorough washing post brine.
Osmosis works not only for water, but for the solutes themselves. Water doesn't just (or even initially) move into the cells: salt, in fact, is what initially osmotes into the cells (they have membrane pumps for equalizing sodium concentration across the cell boundary), and then water follows, in order to equalize overall solute concentration. That's why you see the turkey take on water even when placed in a concentrated brine.