请教一个语法很细微的区别

Sb. Claimed to have been the first to do
Sb. Claimed to be the first to have done

请问这2者的区别? 请大家讨论!

claimed to have been the first to do：曾经是第一个做某事的，也就是说，现在已经不是第一了，只是曾经第一而已。

claimed to be the first to have done：第一个曾做某事的，也就是说，到现在还是第一，比如，第一个吃螃蟹的人，永远是第一个，嘿嘿。