So you say 'key expert' and 'came across an Oxford academic'
How do you know it's a key expert? Because he/she call themselves one? Oxford academic - there are a huge number of people connected to Oxford University. It's not the magic all-seeing qualification people think
In formulating vaccination recommendations, panels of experts (likely degree, masters, PhD, post doc or two, lectureship and professorship, or leading role in hospital/research organisation - 30 years or so of experience) come together. Centuries of combined experience and expertise.
They review existing evidence and grade it on quality, things like number of patients, whether the study controlled for confounding factors, how applicable it is broadly - eg. Study that only looked at one ethnic group might not be applicable across all.
They then sort through all this evidence and find consensus on what can be recommended. For vaccines, that will be around timing and number of doses, details of the vaccine, storage, likelihood of complications and side effects.
And this will be regularly reviewed as more evidence comes to light. Guidelines can be national but are also sometimes regional or global.
In contrast, you read a book that was probably published some time ago, and found one study online.
You just can't possibly encompass the scale of information the experts have. They know there can be side effects, there's no cover up, it's just still overall beneficial.
The internet gives people unprecedented access to information but this is not the same as the knowledge of how to process and interpret this information.