Sounds like a real world case of the trolly problem. Either take no action (by giving out no vaccine) and let hundreds die each day, or give out the vaccine and kill a few people each day (assuming the vaccine is causing the deaths, which likely isn't the case anyways).
That trolly problem is a one off. Having a major vaccine lead to serious issues puts all of vaccines into question, creating a far larger problem spanning time. It's already the case that various sub-communities are hesitant to get the vaccine based upon previous experimentation on their populations long ago, such as the Tuskegee Study.
Is pulling the vaccine (with minimal evidence that it's causing issues) worse? How many people are going to turn down the AZ vaccine now, even if there's not actually an issue?