This is exactly why choosing a specific year, such as 1965, is political. It would be intellectually honest if they posted a range, with a large error margin.
Geological and cosmological history is filled with hypothesized events and broad revisions in the face of emergent (if subtle) proof against common views and norms. Lots of hypothetical place holders aren't apolitical at all. The big bang is pretty political, despite the background radiation that serves as "reasonable evidence" that something like the big bang might have occurred. The truth being that we don't honestly know why a universe would be created through a big-bang-like process, even though it's the best interpretation of the evidence we have access to, lately.
Large error margins are artifacts of incomplete information, and that doesn't mean incomplete information is truly preferable. We have pretty good information about 20th century events, even if the particulars of the social landscape are hotly debated.
We don't have specific dates for when the vast majority of extinctions have happened. We have a rough idea of what the base line extinction rate was for the last million years, and we have good data suggesting that the trend has been up for maybe 10-20,000 years, give or take several thousand years. Picking a specific year, such 9,874 BC, or 434 AD, or 1965 AD, is arbitrary, and a political act.
Arguably, all geological timescales and frames of reference (as named by humans, and thus innately political) are based, not on biological taxonomy and known degrees of species diversity, but rather, on geological records, for which radioactive markers from weapons testing carried out by humans, remains a relevant and valid point of reference that may outlast us.
Really, it's not a political statement just an interesting observation.