Will combining roof venting systems cause short cycling?
Your inspector is correct.  Air should enter at the soffit, and exit at either roof vents or a ridge vent.  With the current setup air could be entering either the soffit vents or the roof vents, and exiting either the roof vents or the ridge vent.  Since your soffits are covered with insulation (because there are no baffles), I'd guess that air is entering the roof vents and exiting the ridge vent.  This means only the air near the top of the roof is cycling, which can lead to problems with the roof including a shortened roof life.

In my house there were originally roof vents in the roof above my garage. When they did a reroof they switched to a ridge vent, and as you can see they covered over the old roof vent openings. 



On a side note: Inspectors are hired by you, and work for you.  They have no reason to lie or mislead you, since they will not gain in any way from it.   In fact, you can probably trust an inspector more than a random person on the internet. Seeing how you paid the inspector for advice, while I'm doing this for free.