Often the double-P spelling shows up in URLs and web headers seen in search results, while only the correct spelling is seen in the actual publication. This happens even on (gasp) a Harvard page. See the naughty URL? It's been my experience that webmasters can't spell their way from a wet sack.
https://cuhs.harvard.edu/procedures/hippa
Your chosen dictionary appears from the T&C to be more of a marketing vehicle. I like Farlex myself. It had the good sense to nudge me in the right direction when I plugged in the wrong spelling.
http://acronyms.thefreedictionary.com/HIPPA
Now if you really want to kill a few minutes, I found a lawyer who once began the etymology of the double-P, also discovering uses of "H.I.P.P.A.A."
H.I.P.A.A. NOT H.I.P.P.A.
Since you are so knowledgeable, please answer the following questions:
1. Who are they? What is their full, legal name
2. What is their legal physical address (no box numbers)
3. What is the address of their website?
4. In what state(s) are they licensed?
5. If you knew who they were, why did you search a phone complaints site for their number?
We eagerly await your reply, the lack of which strongly suggests you are a shill for that phone number.
I think you are wrong that information has to be private I tell you right now that it is a private person with license and that has clear and real privacy that is at the discretion of each person ...