Is it true that children in medieval England were given extra beatings on Christmas so as to "remind them of Herod's cruelty?"

This was on TIL and has a source, but I don't have the ability to verify them. Is the claim true? If not, is there a historical basis for a similar claim?

Sources:

"Gregory observes that it hath been a custom, and yet is elsewhere, to whip the children upon Innocents Day morning, that the memory of Herod’s murder of the Innocents might stick the closer, and in a moderate proportion to act over the crueltie again in kinde." Gregorii Posthuma, 1649. See Cotgarve’s "Dict." and the "Dictionn. de Furetiere." The source is given as W. Carew Hazlitt, Faith and Folklore: A Dictionary of National Beliefs, Superstitions and Popular Customs, Past and Current, With Their Classical and Foreign Analogues, Described and Illustrated. Forming A New Edition of "The Popular Antiquities of Great Britain" By Brand and Ellis, Largely Extended, Corrected, Brought Down To The Present Time, and Now First Alphabetically Arranged. In Two Volumes London: Reeves and Turner, 1905."

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