It's quite common for someone to ask for customer referrals. I think someone who requests this is conducting their due dilligence. Usually a client will ask for someone you did an inspection for within the past month or so.

If I were a client and asked, but the HI told me it was personal information, sorry. - I would look for another HI.

Proper etiquette would be to contact the past client and ask if you can use them as a referal source. If they agree, let them know who may be calling.

Prior to providing the referral to the perspective client you should also let them know that you wish to check with your past client before you give them their telephone number.

There are plenty of questions a perspective client can ask of the referral that would be helpful information.