what about coinomi? Is it the same case - we have to trust what they say or is it possible to verify if the ownership of the keys?
More or less what TryNinja said. coinomi uses standard BIP32 for generating keys.
I use coinomi and like it. Just keep the following in mind:
There have been reports of people getting "hacked" and loosing significant amounts. BUT, (AND THIS IS IMPORTANT IMO):
1) There has never been any independent verification of that by trusted people.
2) At least one of the claims has been proven false.
3) There are many people (myself included) that have at times has a lot of money in both the phone and desktop wallet for a period of time with no issues.
The other side:
1) Parts are closed source so you really don't know what they are doing.
2) The desktop version for Windows (can't comment on other OS) uses browsercore64.exe which is the open source web browser created by Google. So take that info as you will
3) Since it is BIP32 you can have the exact same wallet on your phone and desktop and laptop. Which is really handy, until it's not. Yes, you can do that with any BIP32 but I have seen it more with coinomi. Which is great till something goes wrong. Was your laptop compromised? Did your kids at home do something?
For real money you are best off with a good hardware wallet. Which one is best is a loooong discussion with lots of arguments here.
For having Doge and some ETH and some LTC and some DASH and... all together knowing that there is some risk (you have to determine what your acceptable risk level is) then I think coinomi is great.
-Dave