The 10th, for example, wore red, pointed cuffs in that period. They didn't wear brass buttons (I'm not even completely sure he is), but then again reenactors are rarely perfect.
Anyway, just as grenadier and voltigeur shakoes often had stars on the chin straps (the French is
jugulaire, by the way), so did carabiniers.
Here's a photo of an 1812 light carabinier's shako with star badges and no coloured lace. The metal is white, but I've also got pictures of light infantry shakoes with brass metal. It's not hard to believe the combination of those things was worn by someone. Even if it's not, you were willing to except his shako was wrong before.
Then they have bad sources, cos the Tirailleurs had very distictive white lace.
Is that what you meant when you said it's inaccurate? because they abandoned the white chevrons in 1813 when they adopted the 1812 uniforms.