If Biticoin is running smoothly and there is no disagreement between users, then Stolfi is right in saying that non-mining nodes do not contribute. Non-mining nodes provide verification, but if all the miners are following the same verification rules as the user base (I'm assuming 51% of the hash power is here), then the miners are providing all the verification needed.
However, non-mining nodes allow users (exchanges, merchants, individuals) the decision power of acceptance. Non-mining nodes enable users to decide for themselves which rules constitute "truth" and which branch to follow.
This is important for when there is a disagreement between miners and the larger ecosystem. Miners are free to build a longest chain according to their rules, but users are free to follow a different set of rules even if those rules are backed by a smaller set of hash power and have a shorter chain (by rejecting the rules used to validate the longer miner chain).
If a user led fork happens, then at the moment Stolfi is wrong. Non-mining nodes are the mechanism users use to decide on a different branch (i.e. a BIP101-only branch). After the user led fork was resolved and both miners and users are in agreement, then Stolfi would be right again. Non-mining nodes would not contribute much at that time. At least until another disagreement between miners and users happens again, which it will at some point.
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