The Essex reality star was running late for her interview on ITV's This Morning last Wednesday which meant Paul's feed was delayed; when viewers tuned in for the interview, they saw Sam feeding Paul underneath a towel.
Co-host Phillip Schofield pointed out to viewers it had been Sam's choice to cover up, not something This Morning had asked her to do.
"In case you think we're saying, 'cover the baby up', this is Sam's choice," said Phillip.
"Of course," replied Sam.
Speaking to Reveal magazine, out now, Sam said: "I'm so happy [with the positive reaction]. When I got there, after four hours stuck in traffic, I was panicking and Holly [Willoughby] said, 'Just feed him.'
"Paul was searching for my boob so I just said, 'Is there anything I can cover up with?' They grabbed a tea towel from the kitchen. I'd have been really embarrassed if he pulled off, though, and my whole boob was exposed on live TV!"
Sam, 25, had been on This Morning to talk about her new ITVBe series The Mummy Diaries, which was commissioned after the success of one-off documentary The Baby Diaries, which was filmed in the run up to son Paul's birth in December.
In the first episode, which aired last week, we saw the return of Sam, Paul and Sam's partner Paul Knightley to screen as they navigated the world of first time parenting which help from their families.
It airs Wednesdays at 9pm on ITVBe.
Pick up your brand new Reveal magazine, out now, for more from Sam on the TV show, defending Paul and how sister Billie's pregnancy is going.