A bit of historical background might be good. Blockchain.info has had several high impacting bugs over the years that has led to their users losing funds, like

A bit of historical background might be good. Blockchain.info has had several high impacting bugs over the years that has led to their users losing funds, like biased random numbers and re-used r values. Another bug of this type shouldn't be too surprising. Many people used to recommend against their wallet for these reasons, but on the other hand they haven't closed up shop and ran off yet, which makes them head and shoulders above the average hosted wallet provider. Bitcoin is a very special space.