My first response is to take the rumour with a large pinch of salt, my second too. But for every lower division supporter there is always that nagging worry at the back of one's mind. Ask yourself honestly which of our rivals entering administration would really shock you, not many is my personal response. There is always that risk because so many clubs trade close to the edge for years and sometimes they fall over. I think it's nonsense but trading conditions are awful for everyone at the moment and likely to get worse.
I don't think Eddie is stirring but I do think his general dissatisfaction and anxiety about the club has nudged him into catastrophe mode. He's not alone. In the past this sort of talk would have taken place in the pub, the social club, or on the terraces and a bit more detail would be out and about of varying credibility. I suspect someone has blabbed about an unpaid bill, an argument with a supplier, or some other matter and started the rumour ball rolling.
Edited following 58's post. Eddie's CV is pretty much all taken up with supporting GFC, Kent and England. I am sure his CV would not be inferior to my own but I reserve the right to have my say. Sometimes utter BS and tripe comes from above and us gossipers talk more sense, not always but sometimes.