I'm still very confused about Bitcoin. Now, I opened a wallet from blockchain, ok? And you know, I have the identifier, pass, mnemonic info and etc...
Do I need to something extra? I mean, isn't this enough? Why people are using other wallets?
If you want full proof wallet I will suggest wallet with full validation (you need to download whole blockchain, for now it is more than 40GB and growing).
As recent news shows there can be something called 'split' when some blocks can be invalid and it happen that Bitcoin Core 0.10.x or 0.9.5 are immune to this issue.
With online or simplified validation wallets you can never be sure.