There is a record of a birth in New York that cannot be excluded as a possible record of Zero's birth.
Other information is inconclusive. I don't think he was born on August 4, 1961 either. On the other hand, he might have been born on some earlier date outside the US and then brought to the US during the first week of August which would account for the missing immigration records.
This is simply another part of the equation that ends with a dollar sign--in order to do an adequate research job on this issue, you need resources. You need to recognize that Zero and his supporters have probably spent in the range of $12mm concealing the true record.
Although volunteers here and elsewhere have accomplished a great deal, it isn't very likely that a group of volunteers is really going to defeat $12mm of professional effort.
I would assume that Sheriff Arpiao’s team has some money that private researchers did not have, so perhaps his posse is coming up with more concreted evidence.