Yes, it's a twist on the old slogan 'think globally, act locally'. Bear with it, though; it means something related, but also quite different.
There is a certain degree of equivalence between a Badiouian Evental Site, the situation of mésentente in Rancière's 'part-of-no-part', Agamben's State of Exception, and, (perhaps least of all due to its apoliticity) a Lyotardian Differend. I do not know whether it was Balibar or Agamben who first noticed this. There is an excellent article on the subject of the Evental Site here.
It's sometimes startling to recall that Apartheid, slavery, and colonialism were all perfectly legal regimes. Even the Shoah was fully legislated for well in advance. In fact, a pre-occupying focus of genocide studies has been that the legal framework for acts of genocide always pre-exist the historical atrocities they legitimate, which constitutes in itself a formal, absolute, atrocity. Rancière is therefore far from merely sporting with language when he speaks of 'a wrong that is right': like Agamben, he is talking about situations of legally supported injustice. As leftists, whether we admit it or not, or whether or not it is explicit in our theoretisation, we are all dependent on a distinction between legality and justice. Without an idea or sense of justice, there can be no sense to revolutionary politics.
Just how generalizable this recognition is I do not know, but Badiou seems to have identified the formula under which the distinction is most visible: the Evental Site. Just as, for Agamben, the legal State of Exception (which defines the Homo Sacer) is both the gravest problem and the greatest hope, for Badiou the Evental Site is that place ('on the edge of the void') where organisation and true (revolutionary) political subjectification is possible.
With respect to Grenfell, for example, it is easy to see how the tragedy occurred, and difficult to see how things might have gone otherwise. Human voices were effectively put on mute; dissent from the dominant opinion was simply ignored or alleged not to exist; legal recourse was denied to residents; complaints were met with strong-arm threats and silencing strategies on the parts of the powerful. Here the structure of the situation is Evental: elements of the situation were on the edge of the void because they 'belonged' without being 'included'; they were always present but their political power considered from above was unaccounted-for, always rendered null in advance by dissuasion and threats.
Yet within this situation, in which human subjectification and the political representative link was denied to residents by those financially invested in keeping them quiet, residents formed their own collective and attempted to speak out. They attempted to give themselves a voice and make themselves known. One of these efforts was the Grenfell Action Group. When people in an Evental Site, denied voice, give themselves a voice, they are participating in revolutionary subjectification. Just as those denied human rights in detention camps around the world demanding due legal and political representation, refugees or workers deemed illegal, sans-papiers, or mere 'survivors', all contesting that they be acknowledged to be fully humanized and not pseudo-animal in status, so the residents of Grenfell were in the process of what Badiou regards as proper political subjectification, i.e. the formation of a subjective body of fidelity to a truth (in this case the truth would be something like: 'justice exists' or 'we have a right to rights'). This is far from a trivial theoretical observation. It means that, since truly public social housing has all but disappeared, the rentier and the private landlord being the ascendant figures of contemporary and near-future capitalism, and with coming generations unlikely to buy their homes, local bodies such as the Action Group are of extreme significance in our era. Perhaps even to the same extent that industrial workers' unions were in the time of bourgeois-owned factories (which constituted the Evental Sites of their times). This is all the more the case when the labourification (or monetisation) of everyday life is considered in closest scrutiny. It is not so much the worker, but the life-as-worker — the one whose ordinary living of their life constitutes an upwards revenue stream (via rents) — who constitutes the next historical subject.
Had the Grenfell community been able to reach the wider electorate, or perhaps federate with other similar communities without official voice, amplifying their own politically autochthonous voices, perhaps the tower fire might not have been inevitable. An Event was, at some point, perhaps possible. It is important that this failure is not regarded merely as the structural 'democratic deficit' of our neoliberal, democracy-abreviated times, but also at a much more grass-roots level a failure to rouse a wider context for concern, to federate, and to ally. A failure to see past the privatization of "issue" politics into groups of people concerned only with single issues affecting their members. A failure on the part of the left to regard "someone else's problems" as being a problem for all; a failure to think generic truths ('justice is a thing worth believing in', 'there is a right to have rights', etc…) in particular situations.