That's actually a truth with some modifications. While most DCP software does include a Rec709 to P3/XYZ LUT, it's not always clear what it does, and how it does it. There's the issue of what gamma to use for the Rec709 (2.2, 2.35 or 2.4), and some DCP software (CineAsset, I'm looking at you) even uses the Rec.709 encoding curve to decode, which is just plain wrong.
And then there's the problem of white point. Rec.709 uses D65, while the DCP white point is around 5800K. You can convert the white point (if you don't, Rec.709 material will look sort of magenta in the DCP), but that affects other colors, often in slightly unpredictable ways.
So it's not really a completely lossless and perfect conversion, although you can get quite close. I'd recommend testing different LUT options and variables.