"Is there any evidence that tweets have meaning? I could easily imagine a world where posters fool themselves into thinking the words they wrote contained their intentions, while readers fooled themselves into thinking they had uncovered those intentions."
As with all natural language, production and interpretation of poems is subjective. Poetry is just an attempt to use natural language without the constraints of prose, in order to accomplish things that are not possible with prose.
Some poets may have a goal to convey a particular idea or emotion. Others may just want to create something moves the reader. Still others may not care about the reader at all. All of these things are okay.
As with all natural language, production and interpretation of poems is subjective. Poetry is just an attempt to use natural language without the constraints of prose, in order to accomplish things that are not possible with prose.
Some poets may have a goal to convey a particular idea or emotion. Others may just want to create something moves the reader. Still others may not care about the reader at all. All of these things are okay.