There really is no need for paranoia.
Press Support Us! button, provide details and pay by credit card or Paypal.
Large organisations such as Paypal are eminently pursuable for privacy breaches, incorrect charges etc ... so they are much more rigorous with getting it right.
This is big business ... and potentially big liability for getting it wrong. They have a privacy policy, and don't 'sell' your details to anyone ...
I am grateful that Paypal have my email address. They alert me for 'unusual' purchases, or security concerns on my account. ie .. the things i expect my email address to be used for.
The fact is that credit card fraud is common, and these companies need to protect themselves (and you).
It strikes me as somewhat obtuse to expect organisations like this NOT to collect such info, and to enable your credit card to be debited without any means of verification.
Are we sure that we're not being 'just a bit' difficult here?