His Eminence is exactly right on this. The current Holy Father, in his work from 2000, The Spiritof the Liturgy, goes into detail on this, which I perhaps can re-examine later. We are primarily speaking of the Latin Rite here, for the Eastern Churches have their own traditions which date back to Apostolic and Patristic times.
If you need proof, or just want to look at how Holy Communion should be received:
And now for some awesomeness: I met His Eminence this past summer at the 'Church Teaches Forum,' at the Galt House. It was such a blessing to receive on the tongue kneeling from him. (It was also such a blessing to receive his blessing!) He asked about my vocation discernment, and I gave my usual sheepish answer. After dinner, I came back and talked to him about my thoughts on the need to be a good husband and father, whether it be to a woman, or to the Church. I cried, and explained to him that my model in all of this was Thomas Vander Woude. I also told him that I hope to promote his cause for canonization next year.
Photo credits to Mom!
He's such a wonderful priest; I consider him to be the only possible American cardinal who could become the next Pope. His Eminence is the right age, presuming Pope Benedict lives a few more years Deo Volente, and is of the same theological and liturgical line of thought.