the first complete eukaryotic genome?

In science news this month, a paper in BMC Biology is reporting (Nozaki et al) the sequence of "the first nuclear-genome sequence for any eukaryote that is 100% complete." This might come as a surprise to many scientists, even genomics experts.
The new genome is the red alga Cyanidioschyzon merolae, and it is just 16,546,747 nucleotides long, including all 20 chromosomes from telomere to telomere. The genome had been published previously, but it had 46 internal gaps (totaling 46,469 nt) and the telomeres were missing. They also discovered that about 20 kilobases were mis-assembled previously, a common problem that I've written about elsewhere (see my editorial with Jim Yorke, "Beware of Misassembled Genomes", available on my home page.)

But wait a minute, you might ask (as I did). What about the yeast genome (S. cerevisiae), originally published in 1996 as the first eukaryotic genome? I thought that was finished some time ago. It's true that there have been many published corrections since 1996, but I know the telomeres are present on most (all?) of the chromosomes. And how about the nematode C. elegans - it was published in 1998 while still incomplete, but about four years later it was announced as complete (see the link). These papers are cited by the new paper, but oddly, it doesn't explain what is missing from these earlier "complete" genomes. And I think we finally finished the malaria parasite, Plasmodium falciparum, although the original paper (which I was a part of) appeared in 2000, before all the gaps were closed.

Of course, most genomicists know that the human genome is still far from complete - all the telomeres and centromeres are missing, and there are several hundred other gaps - but I am a bit skeptical of the claim here that the red alga C. merolae is the first complete eukaryote. Can anyone out there tell me why I'm wrong?