The Great Toilet Paper Scare of 1973
priceonomics.com
priceonomics.com
The government instituted price controls and shortages were the result. We even had shortages of natural gas, which, at the time, came entirely from with the US.
In this environment, such a rumor was not hard to believe.
Actually I think in these situations the problem is that individually the people are acting rationally. The only way to be more rational is to act as a group, which requires reliable information, and/or requires government (or other similar bodies/structures) that you trust with your basic needs.
When the gov say there isn't a petrol shortage you know that in the past they've said this because there is and they're trying to avoid panic. Unless you've got better info "panic" buying seems quite rational to me.
If it only costs a small amount to buy lots of toilet paper but not having any would be a major inconvenience then any suggestion that might pan out to be true is worth following - you're down a few dollars that you would have eventually spent any way.
Isn't it precisely that people aren't being idiotic that makes such runs on resources [or banks] so difficult to handle: you go on TV and say "don't panic buy or we really will run out" - well that just tells everyone to make sure they buy it first, because everyone else is buying and so "we really will run out". Your best bet is to have trustworthy news reporters that can show date verified information contradicting the shortage - eg warehouses packed with toilet paper that the experts say is enough to last x months of normal usage.
Not looking after your short term interests leads to privations.