Not true. By default the iphone will leave mail on server. There isn't an option to change that.
It's the client on your computer you need to make sure you tell it to leave the mail on the server for at least a few days (in case you happen to be unable the get data connection iphone) so that if the email is checked on the computer, it is still there for when the iphone checks it.
Might depend on her mail provider? I use gmail, set up as an exchange account--this way my phone and my laptop are always in sync. Anything read on my phone is still in my mail account online, it's just marked as read.