Choice is an Australian consumer watchdog and review magazine.
In a 2009 article titled Thread count is marketing spin, they warn that the published thread-counts may be misleading.
(This is a slightly different argument to "Thread counts are unimportant.")
In particular, they highlight that there is no standard for how thread-counts are measured:
> Since there is no legal requirement for manufacturers to state how they counted the threads, the term is almost meaningless.
They go one to warn that two-ply threads may effectively double the thread-count without necessarily being less coarse, and the coarseness of the threads may make similar thread-counts feel different.
Linen Place is a retailer (and therefore might have a conflict of interest) but in their explanation "The Truth about Thread Count", they explain the (US) FTC have made rulings about the definition of thread-count (and how the manufacturers have responded), so the situation may be different by country.