Hmmm, true....Tolkien apparently translated "Fimbrethil" as both 'slender beech' and 'slim birch' in the Appendices of Lord of the Rings, so I can see the arguments either way.
In the appendix of the Silmarillion, 'brethil' is specifically translated as 'silver birch' (but of course this appendix was arranged by Christopher Tolkien, not JRRT), and on the map of Beleriand, it's the 'birchwoods' of Nimbrethil. So that was why I was thinking birches, but I think that Tolkien himself would have given more weight to the version he published first, so the fact that both are in the Appendices of LotR means there is strong justification for either.