Actually it's not that hard to understand if Obama Sr. had found out about Stanley Ann's liaisons with Frank Marshall Davis and was therefore doubtful that the baby was his after all.
He didn't want to admit in writing in a signed document that the baby was his.
On the other hand, when they called him and asked him about it, he discussed it orally, as obviously he was not going to divulge the whole Frank Marshall Davis business with some dude calling from the INS.
Yes, I noticed that. For some reason or another, Jerome Corsi does not mention it, neither in this article nor, IIRC, in his book "Where's the Birth Certificate?"
Could be that (1) Obama Sr. was completely unaware of baby Barack's birth; (2) Obama Sr., for some reason, didn't want to axknowledge baby Barack as his child; (3) Barack Sr. thought that he wasn't the father; or (4) the real DOB was sometime later than the date Obama Sr. completed the INS application for extension of stay.