Let's think about this for a minute... while usually agreeng ith The Builder, I think that your description of the condition of the existing floor to be revealing. If the floor, as The Builder suggests, has shrunk over the years due to contraction the base cause of which was the boards drying out (also as Builder states)... then there's plenty of ventilation below your floor, else they wouldn't have dried so over the years.
Look, your going to lay a material on the floor that's probably mostly a foamy plastic that will additionally reduce the ingress of moisture, over which you will lay the floor. So, in my opinion, unless it's pretty easy to do, I wouldn't expect that you'd need additional ventilation. The ventilation also introduces cold air in the winter, making the floor even more difficult to keep warm.
One thing I would check is to see if there's plastic layed on the area under your floor, if it's just bare earth... again, to keep he humidity down. If it's finished, no worry...
Be sure to leave 1/4 to 3/8 inches around the entire perimeter of your new floor to account for expansion and contraction and don't nail the base board over the gap tightly! Best of luck!