I'd agree it can be interpreted that way but it uses different wording and there is have been different rulings. To elaborate:
Hazard : (Column, Wall, Rubble) - The first time during each attack a model is pushed into base contact with a hazard it gains one fatigue.
Wounding Hazard : (Spikes, Blades, Fire) - The first time during each attack a model is pushed into base contact with a wounding hazard, it suffers 3 damage. This damage ignores ARM. A Wounding Hazard is considered a hazard.
Lethal Hazard : (Cliff, Pit, Deep Water) - If any part of a model’s base touches a Lethal Hazard, that model is defeated. Mark any remaining vitality boxes and resolve their effects (if any). Then remove the model from play. Any additional successes after a model is pushed into a Lethal Hazard are lost.
The first two say that as the result of a push they take effect. Lethal says that if you touch base to hazard, poof gone. I do see that THE LAST LINE says "After a model is pushed" but that is to relay that you lose subsequent successes after a push if they go in the pit. Meaning displacement and shifting, or even the atlas throw can be used to trigger its effect.
Hazards also requires you to "declare an attack" for the push to work for the first two.
viewtopic.php?f=20&t=38424Sulla and Ywain cannot use exploit or rebuff to cause a model to take hazard or wounding as RRG_Walker ruled in one of my earlier posts. Lethal would still occur so far as the wording allows and I don't believe it has been contradicted.