That said, Nathan Winograd's HuffPo article amounts to little more than malicious hearsay and it is incredibly biased, leaving out critical information in favor of whipping lazy readers into a furor.
The core of his argument is based around documents filed by PETA's shelter to the state indicating the intake, adoption, and euthanasia rates of their "animal shelter".
Note the part of his discussion which centers on the fact that by calling their operational a "shelter", there's an understanding that they'll actually try to adopt out adoptable pets. The numbers they've given don't appear to support an active adoption policy.
Now, if as you say PETA is running this "shelter" purely to take in sick, injured or incurable pets so they don't get abandoned, then no problem. As long as they stop calling it a shelter and make sure that anyone turning animals over to them understands that they're almost certainly going to kill it. Or, as some cases indicate, just let it finish dying on its own in a stack of cages.
As for the argument that there are worse shelters and no-kill or rescue operations... yes. Yes there are. Unimaginably worse. The vast majority of them get into the state their in through a huge lack of resources (financial, staff, marketing, etc), which is the exact opposite of PETA's situation. That makes PETA's shelter an interesting case study... how can a shelter with all the money, volunteers and a powerful PR machine behind it kill 9x% of the pets that walk through the door?