Thank you for checking. So from your experience and mine we can safely infer as follows:
(1) When the address associated with the Dreamhost customer account is outside the EU, the form is pre-filled with blank;
(2) When the associated address is in the EU, the form is pre-filled with the contact details which Dreamhost has for the customer, including the primary email address used for logging in to the Dreamhost account.
As you mention, in either case the customer can then fill in or adjust the form fields as desired. However, this is not the main issue for this thread, at least as regards the OP, which is as follows:
to pre-fill the form with the customer's account contact details, especially the primary account email address, is an inadvisable pre-set, unless private registration is offered and is pre-selected by default.
In post #2, Ipstenu suggested that "There really isn't another decent option."
Well I really do very much appreciate the more frequent input from Dreamhost staff that we've recently been getting in these forums.
But not only is there a much better option, but the current procedure is not even good.
The better option is that (IF Dreamhost is unable to offer private registration for .eu registrations, which is an ongoing question of some interest), then at least some of these pre-sets should be blank (and if appropriate, the fields can be marked as required).
(Plus, for convenience, it would be quite OK to provide a check-box, unchecked by default, which says "Use my Dreamhost contact details", which would fill in all the fields.)