Monty's reason for opening door number #3 (or any door) in the second round does not matter. With the problem as stated (1 car/2 goats and the locations can't change) then if you see a goat on round 2, you should always switch.
In the first round you have a 2/3 chance of picking a goat. Equivalently, you have a 2/3 chance of there being a car and a goat behind the other two doors.
Monty's choice in the second round doesn't change that.
If you picked a goat in the first round (2/3 chance), you will always win if you switch (since the other goat has now been eliminated). If, for any reason, you are shown a goat in the second round then you should switch.
Switching gives you a 100% chance of winning in the case of picking a goat in round 1 and seeing a goat in round 2. Switching gives you a 100% chance of losing in the case of picking the car in the first round and seeing a goat in round 2. Since the problem states that we see a goat in round 2, pick the scenario with the highest likelihood (2/3 chance of picking a goat in round 1).
Monty's reason for picking the door doesn't matter because it has no effect on the probability you picked a goat in the first round. And, as long as he shows you a goat in the second round, it doesn't matter why he did that.
(The only alternative would be Monty showing you a car, in which case your choice doesn't matter, unless you care about which goat you get, since you can't win the car in that case.)
Now, as a systems engineer, I would quibble with the way the second sentence of the question was worded: "If you want to win a car, you should switch". If this is read as "Should you switch to obtain a 100% chance of winning?", then there is no answer to the question, neither choice will produce that outcome. A better wording would be, "Will switching your choice increase your chances of winning the car?", in which case you were correct and the answer should be "Yes".
Were I to have this situation occur during an interview, since I believe you are also interviewing your new boss, I would calmly walk through my reasoning (as above) and see how they react. The best possible reaction would be, "Huh, I think you might be right. I'll have to look into this some more." I would be very concerned if they seemed upset at being challenged, or refused to consider the possibility they could be wrong. A good manager wants to hire people smarter than they are and should be willing to hear them out without being threatened.