In this case the information is mostly okay, with some caveats. Morels certainly don't fruit exclusively when a tree is dying (this blog doesn't quite assert that, but it does highly emphasise the dying trees part so I can see how you would take that away) and it's important to note that the trees death was caused by a separate parasitic fungi and not the morels. They're fruiting in an attempt to spread their spores before they go down with the ship, so to speak.

Personally I'm a little skeptical about the old timer stories and the conclusion drawn from them, but I live on a different continent with completely different species of fungi so I couldn't say for sure. Over here our most prolific morel seasons are always when the temperature is mild, there have been good rains and the forest is happy and healthy. From an evolutionary perspective, this makes perfect sense. The fungal spores have a much better chance of establishing new colonies when resources are plentiful. A symbiotic mushroom that only fruits when all its symbionts are dying around it is going to be naturally selected out of existence.