That isn't a study, and doesn't claim to be one. It is a case report, as stated right in the title. Case reports have "n=1" by definition.
As for being able to "safely disregard" it... an insufficient number of data points doesn't mean that at all. It means you can't draw conclusions one way or another.
Let's put it this way: your team has a new chemical that's supposed to do (amazing thing). You decide to test it on yourselves. The first guy takes it and dies instantly.
Do you then say "Hey, 'n=1', so I can 'safely disregard' the fact that Dave just keeled over." and take it yourself?
I think not.
To be clear here, I think the COVID-19 vaccines deployed in the United States are both safe and effective -- but the solution to bad statistical reasoning is not even worse statistical reasoning.
A scientist working on this topic should obviously not disregard anything like that. They should know how to interpret and filter such events.
I was speaking as and for random people on a technology internet forum where "$person got a vaccine on date ABC. $person got diagnosed with diabetes on data XYZ." has absolutely no merit discussing as causation or mental trigger that there might very well be "serious side effects" as stated by OP. I am sure many people died within minutes of receiving their shot because of simple statistics.
Also you went to paint a extreme example without any need. Please don't do that. No one died instantly, that's a huge over-exaggeration of what the linked paper is about. If you want to speak with analogies, maybe "1 person who bought this item also bought that item" versus "people who bought this item also bought that item" might be more suitable.
You made it sound like it was anything meaningful.
There is a lot of research into side effects by big and respected institutions, funded by governments. It is a very popular research theme with lots of potential reward for solid studies.