Matt Barnes refuses to back down from his claims that something romantic went down between him and Rihanna -- telling TMZ Sports straight up, "I'm too grown to lie."

The NBA star caught heat from RiRi herself back in August -- when he told us he and Rihanna had gone "past the crush stage" together -- with Rihanna claiming he made the whole thing up.

But here we are ... in October ... with Barnes sounding like George Washington, insisting he can not tell a lie!!

So, who ya believe?