I've had one of those bracket type bars for the past 9 years. Has never fallen off although I only weigh 140-160 lbs. The one I have can support up to 300 lbs. They are definitely safe if you aren't jumping and grabbing on it and otherwise being careless. However, on the one I have have at home, the brackets are about twice as long as the ones in the link. Not sure why those are so thin. I'd recommend you spend some more money and buy a higher quality bar.

E: https://www.amazon.com/gp/product/B00B1XJFEW/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B00B1XJFEW&linkCode=as2&tag=pullupbarss.com-20

This one also has stubby brackets which I'm wary of... but it supports 300 lbs instead of 220.