Doing, allowing, and intrusion
Woollard's argument begins from the Lockean/libertarian idea that society consists of individuals each walking around with a "private sphere" that belongs to them (consisting, at minimum, of their own body and its abilities)**. From the claim that it's wrong, all else being equal, to intrude on someone's private sphere, she derives a justification for the do-allow distinction. To do something -- say, pushing a boulder down a hill onto someone -- intrudes on their private sphere, which is bad. But holding someone responsible for allowing an equivalent harm that they could have prevented -- say, they could have pushed a junky old car in front of a naturally-falling boulder to save the would-be victim's life -- intrudes on the allower's private sphere. It makes the allower's property subject to being commandeered by society to help others.
The first problem I see here is that the injunction against doing harm intrudes on the do-er's private sphere too. It limits what you can do with your property, and opens you to claims on your property to either forestall harmful things you have set in motion or make recompense afterward. So why should the imposition involved in condemning doing be less worrisome than the imposition involved in condeming allowing? It can't be because there's a greater total amount of imposition involved -- the balance is simply shifted to imposition via moral responsibility rather than imposition via effects of bad things that are done or allowed. I.e., relatively more loss of property to boulder-blocking and less from getting squashed by boulders in a do-allow-neutral system than in Woollard's proposal. As far as I can tell, the only justification can be that doing is morally worse than allowing, thus sanctioning more interference to put it right -- but that's exactly what Woollard hoped to prove.
Another angle that presents a problem is the perspective of the third-party observer who can't interfere in the bad events, but can assign responsibility and blame (and possibly punishment) to the participants. It is this third party who is potentially imposing on the allower by demanding that they stop allowing. But that observer is also allowing the victim to be imposed on by the bad event if they accept Woollard's advice. That is, the idea that it's better for the victim to get squished than for the bystander to have to put forth the effort to stop the boulder rests on the idea that the third-party judge is bound by the do-allow distinction (allow the squishing versus do the demand to intervene) -- but again, that distinction is precisely what the argument is meant to justify.
*In the original sense of "assuming what it sets out to prove," rather than the modern sense of "raising a question."
**I'll accept this conception for the sake of argument, though I think it has significant flaws.