People have been confusing
Emily and
Amelia for hundreds of years. This is a case of two names which had different origins and "fell together" because of their sound, resulting in the creation of intermediate forms such as
Emilia. The youngest daughter of
King George III of England was officially
Princess Amelia but was also known as
Princess Emily.
Since the confusion has lasted so long, there MIGHT be some slight justification for saying the origin of
Amelia contributes to the modern name
Emily and so is part of its origin. But it certainly would be incorrect to say
Emily does NOT also derive from the Latin word, so "rival" is certainly part of its original meaning.