I don't know anything of that author's claim, but the largely accepted reason for lack of armored commitment was that large maneuvers had to have come from high command. Whether it was due to confusion over the airdrops and status of troops and objectives, officers being absent from the field, or in infamous cases, German high command being asleep hundreds of miles away, no major movements happened that could have taken advantage of any sort of major strategic initiative.

The most well-known story is probably that of the 21st Panzer Division. They were staged in Brittany with the plan to use them as a counter-attack to any sort of invasion of Normandy. Though in a place to endanger British landings, they were ultimately ineffective due to a mixture of allied strategy and German bungling. Due to confusion, lack of intel, and lack of leadership, they either sat motionless, committed insubstantial amounts of troops to objectives, or would receive conflicting orders.

There is one account I've read of 125 Panzergrenadier Regiment being ordered to attack a bridge over the Orne captured by British paratroopers, but again due to conflicting orders, a small detachment was easily beaten back by a mixture of British maneuver and firepower, among that being unspecified "bombardment." Perhaps your author saw such accounts and tended to focus on such more appealing factors as straight combat for the outcome of operations. Most of the information I have is coming from Hans von Luck's memoirs.