It was only in the early 19th century that the English started pronouncing the H in herb, according to the OED. Originally, it was erbe (Middle English, Old French). Thus, when the English settled in America, they would have taken the then current ERB pronunciation with them. Many 'obvious' Americanisms are in fact Elizabethan English, for example 'I guess he just gotten mad' for 'I think he just became angry'.