Marshall said the Tigers admired May's honesty after his star front-rower appeared on the Unscripted podcast with ex-NRL winger Josh Mansour.
May, who was mysteriously cut by the Sydney Roosters in 2024, remains unsure why he is unable to get a look-in by the NSW State of Origin set-up despite becoming one of the NRL's leading props since joining the Tigers.
The 27-year-old claimed he and his brother Taylan had been blacklisted by the NRL's social media team - a suggestion League Central has denied - and said his loyalty was to Marshall and not to the Tigers.
"Loyalty is a two-way street. It means everything, it's what you want your players to be," Marshall said.
But the Tigers front-rower also accused Matt Cameron of referring to him as a "gangster" when May met with the Penrith chief executive about signing with the Panthers in 2022.
Penrith face the Tigers on Sunday and Marshall said: "As a game, we want players to be honest and express themselves and be who they are, and then when they are who they are and tell the truth, we don't like it.
"One thing that I love about Terrell is and what we want (is for) him to be himself and express himself.
"He tells the truth and sometimes people don't like that, but that's who Terrell is and we love that part of him.
"But what he says is, that's up to him, and I want him to say how he feels."
May is listed to start against the ladder-leading Panthers (11-1) on Sunday as the Tigers aim to keep in touching distance with the NRL's top eight.
The Tigers will be without Alex Twal after he picked up a knee injury in last week's win over Canterbury that arrested a nosedive in form from Marshall's side, who boast a 6-5 record in 2026.
"Winning softens your mindset and it has the ability to make you think you're going better than you are," Marshall said.
"We had a three-game losing streak where we let in almost 40 points a game that I wasn't happy with.
"It's a good reminder to us that even though we won on the weekend, we've got to do the fundamentals well and not feel too good about ourselves."
