Diría que es mejicana (mehicana), con sonido de J española. I would say it's Mexican, with Spanish J sound. I am Chilean I do not know what the Mexicans say.
I watch Univision and even in Mexico City, they pronounce it, "Me-he-cana." The man saying it has it right. The woman saying it doesn't.
I think it's pronounced like "mehicana" but a slight throaty sound on the 'h' part
It should be pronounces that way. I grew up in the SW US. The Spanish pronunciations are not the same as in Spain. Perhaps she is represents a different region?