Yes the vaccine has been proven to be safe for most adults in the short-term. But blanket statements like this over-simplify the reality of the situation.
People need to be aware that for certain sub-populations (eg pediatrics & pregnant women), there is insufficient scientific evidence - in terms of clinical trials and longitudinal studies - to conclude that the benefits of vaccination always and universally outweigh the risks.
Until consensus has been established in the scientific literature - and even after that - everyone should be making their own decisions based on personal risk evaluation with the consultation of doctors and other medical professionals.