Can a 40amp breaker be used safely and without issue with a 40amp device on 6AWG wire?
Your "electrician" is not one of the brighter bulbs in the pack.

The 40A is to protect the wiring and the device.

If the wiring is AT LEAST 8Ga then it's adequate to protect the wiring. It also protects 6Ga, (or 500 MCM for that matter) just fine, and it properly protects the device at the end of the wire just fine. 

"Ohms law" has squat to do with this. You could have a cooktop located 3 feet from the breaker panel and connected with 8 Ga or one located 100 feet from the panel and connected with 6 Ga - the 8 Ga would have (much, about 20 times) lower resistance, because of the wire length. Upsizing wire for longer runs on heavy circuits is actually quite normal. As stated, not a particularly knowledgeable electrician you have there.