Unless I'm reading it wrong, SERM is doing it correctly (and in a way that jibes with your attachment), although they seem to have made a mistake in flipping their L1 and L2 terms in the equations vs what they show in Figure 1.25 (but proceed to use the correct numbers in the calcs).
Just walking through the SERM example to see if I'm missing something...along the 28-ft long span, the "beam" for checking shear is 24' wide (which means they're taking the entire width of the frame tributary to that column, correctly). Similar to an actual beam, the critical section is d from the face of the column, or "0.5*span - 0.5*column width - d" from the center of the span, and the shear force is the total trib load on the portion from there to midspan. This matches with your attachment and with how you'd do a true beam, from what I'm seeing. Then they seem to calculate capacity correctly, using the 24' width.
The other direction only has a 24' long span (smaller shear load than the 28' span), and has a 28' width (higher shear capacity than the 24' wide span), so that direction does not control by inspection.