Language family trees

 From <http://www.einst.ee/publications/language/history.html> (from
the website posted by Jim Grossman about Estonian cases):

--
A significant proportion of linguists no longer subscribes to the
theory of a language tree, widely approved only a dozen or so years
ago. According to that theory, all Finno-Ugric languages, similar to
Indo-European and other language groups, have developed from one
proto-language. Consequently, doubt has been cast on a large number of
assumptions about when changes occurred in pre-written Estonian, and
about the time when the characteristic features became established.
Several hypotheses about the development of the Estonian language
during the earliest period of development up to the 13th century are
now also considered to be of dubious reliability.
--

And also:

--
The only existing attempt at reconstructing the North Estonian language
has been presented by Alo Raun and Andrus Saareste. Nowadays,
specialists consider similar reconstruction too dependent on the
language-tree, and the Estonian thus restored close to Finnish to an
unacceptable extent.
--

Is this saying that there's doubt as to whether languages evolve from
others? Do I understand this correctly? Is this actually true (i.e.
that people think otherwise)? How do these people explain things like
French, Spanish etc. which have diverged in historical times? Is this
some weird form of nationalism, or creationism applied to language? Or
do they actually have a legitimate, explainable alternative? And how
many is 'a significant proportion'?

To say I'm amazed is an understatement (but then, I've been amazed
before, like when I heard there really were creationists complaining
about evolution being taught in American schools). Will wonders never
cease?

Tristan.

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