Zaher1988,
There is, indeed, a small discrepancy here. The first email you posted suggests they would restore your original password (as Cookie stated, this may work by swapping a hash, meaning they wouldn't actually know at any point what your password is). The second message suggests your password would be reset to a new one, which would be emailed to your alternate email address.
I don't know why there are two scenarios -- perhaps they can do it both ways, perhaps one of the support agents made a small mistake describing it. However, I think they are consistent on things that matter, which are:
1) They will not access your account without your explicit permission, which should be comforting to you.
2) They are
not asking for your password.
The difference between them using special access rights to view your account or change your password, and them asking you for your password, is that the first creates an audit trail and doesn't expose you if you've been silly and used the same password for many accounts at many places. It also prevents them from keeping your password and accessing your account for who-knows-what purposes outside their job, without your knowledge.
I am not sure why you have as much of a problem with this as you seem to. Ordinarily, I am first and foremost concerned with individual privacy, but sometimes it is necessary to see the problem to fix it -- and they are doing it right and asking for your consent. If there is any information stored on your account that you would be uncomfortable with someone seeing, you have the opportunity to delete it before you tell them it is okay with you.
There are times you have to trust professionals who are just doing their job. That applies as much here as it applies to your doctor.
