You are absolutely right, I would say that how the interview question was posed and the example given is very misleading, if not outright incorrect. Here is why:
Hedging does not increase your risk in this particular example: You take on delta exposure by buying the short dated option outright. Thus buying/selling underlying (put/call) in any case will reduce your delta exposure, hence risk of changes in the underlying, given you hedge the right amount and at the right timing (this i venture is impossible to generalize as it applies differently to each case). Now, you are long gamma but being long gamma does not guarantee at all that you end up better off not hedging initially. If your boss instructs you to be at all times almost perfectly delta hedged (most French bosses are anal about this, probably because they are horrible delta traders) then you hedge, period. It reduces your delta exposure, hence risk in moves in the underlying. It is complete nonsense to start arguing in retrospect that no hedge may have resulted in a better payoff because the underlying followed a price path not anticipated earlier.
I concur with Strange that there are often better ways to hedge than always going through the underlying but I disagree with him that it poses a "painful moment" to market markers. Market makers who are dependent on the market moving in specific ways are probably very bad volatility traders. Your job as market maker is to earn money from the bid/offer spread and to reduce your risk exposure to lower moment greeks, given it is feasible and cost-efficient. The other times you, as market maker, attempt to benefit from what you perceive as mispricings in the option valuation. Thus, hedging the long options position with the underlying reduces your risk, period. There are obviously exceptions to this, for example, when the underlying is so extremely illiquid that it would be prohibitive to hedge/re-hedge frequently. But it has to really be analyzed in context. But if the interview book looked for a straight forward answer which applies to most cases then hedging reduces your risk, simple as that.