Clara, this is one of the typical rental scams out there - you were wise to question it.
Report the email to trulia - I believe there is a report button for that purpose.
Be wary of any far fetched stories like this one. The scammers always claim to be out of the area with elaborate stories.....next you would be asked to wire money for the keys. They come up with all kinds of stories as to why you can't see the place in person..........the biggest tip off that this is a scam is that the rental amount is usually way too low - too good to be true...because it isn't true!
Don't be lured in because you see real photos...they often cut and paste photos from real listings.