The Short Version
No credible evidence supports the assertion that Iran declared it would negotiate exclusively with Barack Obama. The JCPOA was a multilateral P5+1 process involving Secretary Kerry, Foreign Minister Zarif, and six world powers—not a personal Obama channel. Iran's post-Obama refusals to negotiate cite distrust of specific leaders like Trump, not a declared "Obama-only" policy. No verified Iranian government statement naming Obama as the sole acceptable partner exists in the evidence record.