It's recommended that people wait a few weeks after recovering before getting the COVID vaccine, so they probably wouldn't offer it to you immediately in the hospital if you tested positive: https://www.who.int/emergencies/diseases/novel-coronavirus-2...
But I'm not going to hold my breath on you being able to actually support your statement.
Is it? What do you imagine would prevent it from happening just like I suggested? Can PCR tell the difference between live virus that's causing illness and dead virus fragments? Do the mRNA vaccines cause spike proteins to protrude out from the normally smooth walls of blood vessels, causing clotting as confirmed by D-dimer tests? Does it take 14 days for a person to be considered vaccinated after getting the jab?
CDC regards as unvaccinated until 2 weeks post treatment. So any acute vaccine reaction is regarded as an unvaccinated hospitalization.