Indeed I do hope so the same. Still, even if it is not true that she's been hours looking at her e-mail, she must be aware that she is using the company resources both in the form of time away from work and internet connection, hardware usage, etc.
Now, I don't think any company minds if you check your e-mail and have a quick look to know if there's something urgent one day.
It is different when this behaviour is repeated regularly and it does take time from your regular work.
I'm telling you this because what she may think that it is a fair use, it may not be as such.
The truth is that when we're on the job, we shouldn't be checking our personal accounts. We're working. We're not paid for doing personal stuff. And while we all do it from time to time, it shouldn't be a regular thing.
And for what I've read, for your girlfriend it is. She logs into her hotmail account everyday and leaves it open to know when she has a new mail. For starters, this indicates that she's more interested and pays more attention to her personal stuff than the job itself (which it may be natural, up to a point). For seconds, she may be speding more time cleaning her personal account from spam, or answering to e-mails than she's receiving than she thinks and the company may have a point: she may do her part of the job but not excelling because she's distracted with personal stuff.