"When she came off stage there was this huge sigh of relief from her," Robin told ET. "And not only backstage but the athletes ... there were no snarly looks. There was such respect and they were hanging on every single word."
Caitlyn's new docuseries, I Am Cait, premieres on E! this Sunday, focusing on the Olympic gold medalist's journey since transitioning. Robin weighed in on the show after seeing the trailer.
"She wants to get it right," Robin said. "She's knows there are a lot of people watching and this is a moment that can change the narrative."
Robin has her own harrowing story as her life was saved in 2012 by a bone marrow transplant from her sister Sally. According to Robin, her bone marrow wasn't the only thing that Sally gave her.
"Now I can't get enough of that red velvet cake," Robin said, revealing that she now has her sister's sweet tooth. "I look to Sally and I'm like, 'Thanks a lot.'"
While Robin's spirits were lifted by the athletes at the ESPYS, she found a crop of jocks that are "every bit, if not more so, inspiring" among the competitors of the 2015 Special Olympics.
"Being around these athletes who are competing, and their families, in Special Olympics is a firm reminder that they're like everybody else," Robin, who is hosting the opening ceremonies on Saturday, said. "They celebrate life. They have their highs. They have their lows."