I Stand By My Analysis The Texas Supreme Court actually agreed with my analysis

The court ruled a lack of immunity to the new coronavirus does not qualify a voter to apply for a mail-in ballot. https://t.co/WNt63OIfdb

— Texas Tribune (@TexasTribune) May 27, 2020

Yes, that's what the court ruled, but that ruling means you can still mark "disability" on your application, because nobody's going to investigate it.
1) The application for a mail-in ballot doesn’t require a doctor’s number te ir substantiating medical records; 2) Who’s going to check?

We agree with the State that a voter’s lack of immunity to COVID-19, without more, is not a “disability” as defined by the Election Code. But the State acknowledges that election officials have no responsibility to question or investigate a ballot application that is valid on its face. The decision to apply to vote by mail based on a disability is the voter’s, subject to a correct understanding of the statutory definition of “disability”. Because we are confident that the Clerks and all election officials will comply with the law in good faith, we deny the State’s petition for writ of mandamus.

...

The State has conceded that “Respondents have no discretion to do anything but determine whether the voter is entitled to vote by mail and process the application accordingly.” The State acknowledges that the Election Code does not require election clerks to “investigate each applicant’s disability.” Indeed, the Legislature rejected the requirement of a physician’s proof of disability for mail-in voting applications when it amended the Election Code in 1981.  And the application form provided by the Secretary of State requires only that voters check a box indicating whether the reason for seeking a ballot by mail is a disability. The voter is not instructed to declare the nature of the underlying disability. The elected officials have placed in the hands of the voter the determination of whether in-person voting will cause a likelihood of injury due to a physical condition. The respondents do not have a ministerial duty, reviewable by mandamus, to look beyond the application to vote by mail. Moreover, while the State has alleged that the Clerks are accepting “improper application[s],” there is no evidence in the record that any has accepted a faulty application.

The Clerks have assured us that they will fully discharge their duty to follow the law. We are confident that they will follow the guidance we have provided here. Accordingly, we conclude that issuing the writ of mandamus to compel them to do so is unwarranted.

That is what winning in court looks like.  The Texas Supreme Court didn't act to protect its four members up for re-election.  It said "No, fear of contagion is not a "disability" under the law, but nobody's going to investigate what "disability" means, so fuggedaboutit!"  Which really should be the takeaway from this, if the media wasn't so legally illiterate.  And why did Paxton lose?  Factual grounds:

The [County] Clerks [who were parties to the case, including Harris (Houston) and Travis (Austin) counties] contend, in part, that they lack a duty to “police an individual voter’s claimed disability.” The Clerks also defend their speech before the commissioners courts as accurate attempts to convey information about rapidly changing electoral conditions. The Clerks argue that the State has failed to identify ministerial duties that the Clerks have ignored.

Paxton got poured out, in other words.  The Clerks didn't do anything wrong and are free to accept all applications which claim a "disability," so long as they don't tell voters fear of contagion is a disability.  Yeah, it's half a loaf, but it's better than none, and not the decision reported by the media (even the Texas Tribune got it wrong).  The Texas Dems are already fundraising (or rather fear-raising) on the widely accepted but erroneous interpretation of this decision.  If they had any brains, they'd be telling voters what the County Clerks can't:  claim a disability and stay home this November where it's safe!

(And no Slate, Texas voters don't face prosecution now and we don't need more court rulings on this issue.  a) those prosecutions would have to come from county attorneys following complaints from county clerks.  The Texas AG has bugger all to do with it.  B)  We need better understanding of what the court said, and somebody who isn't a government employee to explain it loudly and repeatedly to Texas voters!)

(My suspicion is Paxton's office said "Hey, we won!" and reporters were stupid enough to take their word for it.  The opinion isn't even that hard to read, and surely they have access to lawyers if they stumble over "mandamus" and don't understand that's what Paxton was asking for and didn't get.  We the people really are not well served by our institutions, including the "fourth estate."  My daughter The Golden Child scion of a lawyer would understand this ruling better than that, and she might ask me what "mandamus" meant anyway.  Ignorant reporters reporting on legal decisions are the worst.)