I would say we all do have it. Most of the material for the Kalevala was gathered from the Orthodox areas anyway, not from Finland or Estonia, as the zeal of the protestant reformation most likely stifled out the oral traditions in more western areas. This is not to say that folk poetry of the Kalevala metre hasn't been gathered in Finland and Estonia as well.
http://et.wikipedia.org/wiki/Kalevala-mõõt
http://dbgw.finlit.fi/skvr/skvr-tietokanta.php
Well, the Kalevala does not mention any modern or indeed accurately determinable ethnonyms, so it seems a bit odd to claim that they were specifically Estonian. However, it is quite possible that all of the kalevalaiset / väinöläiset are Estonians and Western Finns, as some have theorized that Väinölä / land of Kaleva was in Western Finland. The "Väinö/ä"-prefix is a recurring toponym in large parts of Baltic Finnish areas. For example Daugava river is known as Väinäjoki.
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