Trump responded to the release of the long form of Obama's birth certificate with grace and good will. And yes, the showmanship one expects from someone whose flamboyance is his trademark in the business world.
Every time I apply for a job, I am required to provide proof of my citizenship. If someone won't accept my passport, I have the notary-sealed full-form certificate which was used to obtain my passport. When I was issued my first passport, it had a copy of my birth certificate stapled in the back.
The following is strictly Devil's Advocate teasing, not to be taken as meaning I don't think Obama is my rightful President: If the "birthers" want to continue doubting, they still have two more avenues to pursue. Obama's father was a citizen of Kenya, and as such his son could have chosen Kenyan citizenship at the age of 18. I don't believe anyone has searched Kenya's records for Barak Jr.'s possible passport/citizenship papers. When his mother remarried, her husband was a citizen of Indonesia, and moved the family there, and may have adopted his step-son, in which case Obama may be a citizen of Indonesia. Again, I don't recall anyone looking into this either.