[AlotOfReading]

Carbon dating is just fine in non-human contexts. It's commonly used to date non-anthropogenic extinctions, for example. You do need to have a theory about the formation processes that led to the sample and how they relate the sample to the topic under study though.

The dating is this paper is definitely questionable. For one, the extent of their analysis seems to have been taking samples, sending them to the lab (which could have widely varying error checking, I haven't worked with this one specifically), and using stock date calibration software. Unfortunately, they're sampling an area known to be volcanic (which tends to produce older than true dates), with lots of water (matter transports through soil), across a difficult boundary (the Holocene), and a lot of vegetative intrusion (another common error source). They attempt to dismiss the latter by saying it can only make dates younger, which isn't even true, only typical.

The headline would be a tough argument to make even if their evidence was good given the prior history here, but they don't seem to have put even basic effort into it.