On the contrary, while the TNG episode obviously has a core element of the TOS episode in common with it, that core element is removed from the factors that mitigated Federation culpability.
To be fair, however, "Too Short a Season" also provided a rationale for the seeming "necessity" of Jameson's actions: there was no way around giving Karnas what he wanted in the initial instance to save the lives of Federation hostages, and since Jameson could not plausibly either leave those people to die or consign Karnas' enemies to death at his hands, he took the "Private Little War" route.
This rationale is a bit thinner, dirtier and more questionable than the classic balance-of-power dilemma set up for Kirk in the TOS episode, and I think is calibrated to be that way in order to better sell the theme of sin and redemption and to avoid it seeming too
obviously a critique of the Vietnam War analogy of the original episode.
You could say that TSAS played like an updating
of APLW, with the twist that, instead of coming out in favor of Vietnam, it critiqued Iran-Contra.