That's all nonsense: existing personal albums don't go away if you disallow the user to have personal albums. All you need to do is disallow registered users to have personal albums, so the buttons to create and edit their existing uploads will go away. So how do the get there in the first place? Well, the users need to be members of a group that is allowed to have personal albums first and later they become members of a group that is not allowed to have personal albums. This being said, you create a custom group (again in the groups control panel) that is named "Uploaders". Allow that group to have personal galleries.
Then create a new user account for a new customer. As you have created that account (as an admin) you know the access data (user name and password). While being logged in as admin, make that user a member of the "Uploaders" group. This move makes the user able to upload. You then log in using that user account (preferably using a different browser on the same machine, so you don't have to swap back and forth from being logged on as admin and as user) and upload what needs to be uploaded to that user's personal gallery. Additionally, go to the properties of the albums you created as that user and change access permissions to "me only" if you only want that user to be able to access his album and nobody else (except you as admin). This is usually being done if you make sure that the privacy of your customer's shots is not being invaded, but setting album access permissions to "me only" on the album properties is not needed to make the technology working that I just explained.
Finally, after all uploads are complete, log in as admin once more (or use the session in the other browser that you still have open if you heeded my advice from above to use two different browsers) and remove the user from the custom group "Uploaders", so he's only a member of the default group "Registered", which doesn't have permission to create new personal albums nor to edit existing personal albums. However, the registered group still has permissions to access the personal album that belongs to that account.