I don't understand why it would need such permissions. I am using Parallels Desktop 7 on OS X Mountain Lion.
I don't know for Parallels specifically, but I know of at least one app that asked for access to contacts just to get the current user's first name (from the user's "Me" card). The Open Directory database (the users/groups/authentication database) had a "Full Name" field, but it wasn't broken down by first and last name, so if an app wanted to use your first name for default names of things...like "Tyler's VM"...it had to check contacts to find for sure where your first name ended and your last name began.
It's also possible it wanted to look at your "Me" card to try to auto-fill the registration form for you, as a convenience.