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Well no, it doesn't apply here. Even if too many people tried to collect free newspapers to get free heating (and that's a pretty big if), they'll just end up not finding any, and they'll continue heating as always. Free newspapers in a train is not a common good that will be spoiled by or collapse due to overuse the way this happens with the classic shared commons.
You got to be careful with applying the 'tragedy of the commons' thing to everything. There are many things that work when, and because, only a small number of people do it, but usually there is a reason for why not everyone is doing it. If you have someone making biofuel out of green waste that restaurants no longer want, that's "not sustainable if everyone does it", but there's still no automatic tragedy of the commons happening either.
It's absolutely something to keep in mind, but you also run the risk of opposing every 'small' solution on principle, rather than seeing them as part of an overall approach to avoid the current 'big' solution which might be unsustainable long-term anyway.
It applies entirely to the text I quoted.