They would admit to it, sure. There are new alternative vaccines currently under development, no-doubt spurred on by the comparatively minor issues (85/25000000 vaccinated in Europe had clotting) with the Oxford-Astrazeneca, and similarly with the Johnson & Johnson vaccine. Given how rare the clotting is amongst vaccinated people, it's certainly possible for the trials to have missed people that would have been affected.
There are some in Europe who were already considering buying the Russian Sputnik V vaccines, since they weren't able to secure enough as they would have liked. The Pfizer vaccine is still going strong thus far without any issues, too.
Just because there's already vaccines on the market doesn't mean development of other Covid-19 vaccines has stopped.