Wow, just wow.
There are three types of vaccines (loosely) based on the three serotypes of the virus. The HVT based vaccine was back in the day, but is not currently the most commonly used vaccine. However, in countries where liquid nitrogen storage and transport is difficult, it may be the more common vaccine.
The gold standard vaccine is MDV-1 Rispens(CVI988), it's actual MDV. This is not easily obtainable for the backyard keeper like the MDV-3 HVT vaccine is, but it can be obtained. Industry and large hatcheries use either Rispens or a bi-valent MDV-2 and MDV-3 vaccine (sometimes tri-valent with ILT, IB, or Newcastle too). MDV-2 is based on a variant of CVI988 that was found not to be oncogenic. MDV-2 and MDV-1 are actual attenuated (but not killed) Marek's Virus. The only one that doesn't have to be stored in liquid nitrogen is MDV-3 HVT, which is not Marek's, but a similar Turkey Herpesvirus that trains the immune system to react to something that looks like it. MDV-3 HVT cannot pass Marek's because it isn't Marek's. If an HVT vaccinated flock were later infected with Marek's? Yes, they could spread it.
The information that the vaccine is making the virus more virulent is based upon most people's understanding of traditional vaccines and antibiotic resistance. (The NatGeo article is not cited by mainstream science, it was a misinterpretation of a published paper that explained what I'm about to. It only recently regained popularity because it was heavily used as an argument for Covid vaccine related debates.) Traditional vaccines and medicines that kill viruses and bacteria are what makes them mutate to overcome those obstacles (i.e., become more virulent, infectious, or drug resistant).
Biologically speaking, industrial use of the vaccine should have made the virus more widespread, yes, but making it more virulent doesn't make any sense, because a virus wants to spread and reproduce, not kill its host. Herpesviruses are not generally fatal, but they are great at hanging out in a host for its lifetime and popping back up occasionally to spread themselves. Herpesviruses are nearly impossible to eradicate, taming them and managing them is a good outcome; we're not going to kill it, it won't happen.
Sheer infection numbers and wildtype challenges are what give a virus like Marek's the opportunity to mutate. What was the selection pressure that caused the vv and vv+ strains? If it wasn't two strains competing against each other, then finding out what it was that MDV had to mutate to overcome would be an important clue in fighting it. (I've seen speculation that trying to create a "one-shot" vaccine with other diseases may have been a cause, but I haven't had time to look into that theory.) We don't have good information on Marek's because the industry vaccinates, culls the whole flock upon discovery, or doesn't allow meat or laying chickens to live past 8 weeks or 2 years, respectively.
The biggest threat in the spread of Marek's is not bringing in chickens or mixing ages/vaccination status, we should all know better than that already. It's us. Going to the feed store, getting a delivery, visiting with someone else with chickens (not even at their home), hair not washed, a dust storm, a winter coat, other chickens that live upwind, wild birds...all these things can spread Marek's and other diseases like Mycoplasma. Look how long it took for a global pandemic to spread for a virus that can't survive very long outside of a host or in extreme temperatures? Marek's doesn't have those limitations, it's everywhere, and it's been everywhere for a while. We can try to prevent worse strains from other countries by being diligent, but we're not going to stop the ones already here.
We are our only allies in this, and sometimes anecdotal evidence may be all we've got to work with. True science looks at everything, sometimes a major discovery lies in an obscure story or old recollection of an event. Observation is the first step in the scientific method, with a healthy dose of skepticism, but not outright dismissing something unless it has no bearing or is literally impossible; kissing a lot of frogs is in there somewhere too.
