You are correct that verb-ed modifier is not placed right next to the modified entity. In reality, all three kinds of noun modifiers - relative pronoun, verb-ed, verb-ing (without comma) can modify slightly far away noun if the following conditions are satisfied:
1: The information placed between the modified entity and the modifier is necessary.
2: The information placed between the noun and the modifier cannot be placed anywhere else
3: The placement of this information does not cause any ambiguity in meaning.
In this case all these conditions are met:
1: The information "that is an interwowen filigree of mushrooms and rootlike tentacles" is necessary. It describes "a giant fungus".
2: This information cannot be placed anywhere else.
3: There is no ambiguity in meaning. It does not make sense to say that tentacles are spawned or produced by a single fertilized spore. It only makes sense to say that the fungus was spawned by a single fertilized spore.

As another example, see OG12#26 "Emily Dickinson's letters to Susan Huntington Dickinson, written..."
In this sentence, the verb-ed modifier "written..." modifies the "letters" even though the closest noun is "Dickinson". So in this sentence the information "to Susan Huntington Dickinson" is placed between the modifier and the modified entity.

BOTTOMLINE - Meaning of the sentence must be clear. There should not be any ambiguity in the meaning.