OK, you may be right with the heatshield if it's that far away from the towbar although other components may be nearer and they may suffer as the exhaust system is bound to get hotter when towing due to the extra power that the engine is called upon to deliver. However, I doubt whether that alone would be an issue which could affect the warranty unless there is something really vulnerable to heat in the vicinity.
On the other hand, I'd treat the issue regarding the cooling fan seriously. I wouldn't take a verbal statement from anyone, master technician or even the workshop manager, as authoritative if two people have independently said that they have received information to the contrary from their dealers. There's too much at stake to make do without written confirmation.