I don't see how it would help with this, as the study had 32,000 participants. That wouldn't tell you much about rare side effects that appear on the order of 1 per a hundred thousand.

The blod clots are not a rumour, they're there. It's not certain the vaccine caused them, but that doesn't make this a rumour. And the events do seem to be unusual enough that they certainly need investigation.

Doesn't mean the vaccine is unsafe, the events seem to be still very rare, even if they are caused by the vaccine, so the benefits still outweigh the risks. But the events are very serious, so this does need to be monitored closely and needs to be taken seriously. Downplaying potential side effects is not the way to create trust in the vaccine.