How can I use Google Play without storing any Google account information on my phone?

I am using HTC Wildfire handset, but I think following question applies to all Android-based handsets.

My Google Account has been added under

Settings
-> Accounts & Sync
--> Google (under Manage Accounts)

When I click on "Google", I get following options

Sync Contacts
Sync GMail
Sync Calendar

In Accounts & Sync option, I have turned off (unchecked following options)

Background Data
Auto sync

NOTE: I have turned off Background Data, and Auto Sync before adding my Google Account.

I want to get apps and games from Market, but I don't want to sync any of my Google Account data with my phone i.e., there should not be any traces of my Google Account in my phone.

How can I do it?

Answer

Beyond what you've already done, you can't. The Market requires you to have your Google Account added to your phone, and this naturally stores data such as your email address even if you don't sync email.