This seems to be the root (excuse me) of the confusion. When information is communicated, it moves from one place to another. We usually consider communication of information as a deliberate act of some sort, but that isn’t the case all the time. In these botanical instances, no one is really implying intentionality, although some folks are inferring it.
Deliberateness is not my only problem with this whole idea. I also think the idea of “information” is problematic.
In my view, the mushrooms are merely reacting to the presence of nutrients in the tree, in exactly the same way that the tree reacts to nutrients in the sunlight. If you want to say that the tree is communicating information to the mushroom, then wouldn’t you also have to say that the sun is communicating information to the tree?
Sounds as tho you have never had my wife comment on the information your body language is sending! 
This fits firmly in the category of things I have read and mostly forgotten, but didn’t I read somewhere that plants respond a certain way if nearby plants are threatened. Maybe if a caterpillar is eating one plant, surrounding ones will curl up their leaves? Or is that leaves within one plant?
Damn, I wish I retained more of what I read!
If you hit your thumb with a hammer your nerves communicate the fact to your brain. Neither hammer, thumb, nor nerves are aware. Just a travelling chemical potential running up with the bad news.
Information is pretty well nailed by Shannon’s definition. There might not be a lot with the plants and mushrooms, but there is some. The sun falling on a plant is information - one it isn’t night, and two, there is a direction that some plants will respond to. The information is a few bits per day, but that is fine. Just a very low bandwidth channel. One might argue it is the Earth communicating rather than the sun here.
A tree exuding a marker that attracts an appropriate fungus might only encode a single bit (or two) as far as the fungus is concerned in an entire season. But the state of the fungus changes in response to the presence of the marker, and that implies the transfer of information, which is communication.
This article on Defining Biological Communication, from the Journal of Evolutionary Biology, may help in clarifying how biologists think about communication between organisms.
In a way the sun is communicating information to the tree. However, biologists tend to define communication in terms of information transferred between organisms rather than from inanimate sources.
To reiterate, the entire point of the article is that the fungi are not merely reacting to the nutrients provided by the tree, but the tree is an active participant in sending out a signal in the form of nutrients.
if a plant reacts to an event (trauma, nutrient or water source) with defense or seeking action, that action leaves (ha punny) evidence which travels through air/water/soil and other plants react to that; how is that different from me hearing you swear when you yell when you hit your thumb with a hammer.
or an event closer to the types of things in discussion. my seeing you run from the bees chasing you because you’ve stepped on their nest and i start running too before the bees even get near me.
Study: Plants communicate with each other via underground fungi
I saw this very interesting Doco on TV about trees passing information to other trees and those trees reacting to it. They noticed that Giraffes always moved up wind while eating the leaves on their favorite trees. So they conducted an experiment and found that when giraffes started to eat the leaves the tree started to increase the tannin levels to make the leaves taste bitter. Further tests showed that nearby trees that were down wind also started to increase their tannin levels to save their leaves from the Giraffes.
There’s a simple way to differentiate between reaction and communication.
Reaction is when the response is the logical response to the stimulus, when the stimulus is taken literally. Moving to point towards sunlight is a good example.
When the response is to a chemical that has no prima-facie value, in that it does no direct harm or good, but rather, conveys an abstract message that is unrelated to the physical or chemical properties of the stimulus, then that is communication.
Let’s take pheromones used in mammals to indicate that a female is in heat. The stimulus (pheromone) could be any sort of easily detectable chemical, so it’s chemical nature isn’t the cause of the response. Rather, its interpretation as a signal for availability for sex is the cause of the response.
The fact that this signaling may be autonomous and unconscious doesn’t mean it’s not communication, in the broad sense of the term. Ditto for any signals that trees might send through the mushroom network, regardless of whether those signals are interpreted (reacted to) by the network itself or other plants using the network.
On a physical level, though, the response can be pretty much the same as a “reaction”, rather than a conscious conversation. That is, the signals hit receptors, the receptors signal a processing network, the processing network sends signals to affect behavior (e.g., growth). In creatures whe assume have consciousness of some sort, this can be conscious or unconscious.
In creatures where we don’t have enough in common, it’s academic to discuss whether the process is conscious or unconscious.