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[expanded the idea]
Just make sure that the person changing the password is actually the user who owns the account!
Can be done in 2 ways in my opinion:
1. User also enters old password for verification.
2. User also enters some verification-code he got sent via email.
note that point 2 you can also accomplish by using the ability to give them a auto-generated password (wich you allready have). Users can then use point 1 using that generated password to effectively get point 2 :).
get the idea?