Big moves either up or down would be profitable. The only unprofitable move here would be no substantial moves in either direction. (In which case you lose your entire bet, but no more.)
Clearly I lack a basic understanding of the concepts involved.
Sort of like how different companies with the same cash flows can trade at different multiples, otherwise identical options in two companies (or different expirations/strikes in the same company) can trade at different prices because of the opinions of market participants. Volatility traders act when the different prices/error terms are too far apart, counting on the prices/error terms to converge a.l.a. pairs trading.
Since they are trading the error term directly, they attempt to construct positions that remain relatively flat in value as the stock moves around, but are designed to only change in value when the error term changes. That is how they can make money "both ways", because they can profit if the stock goes up, down, or stays the same, as long as the error term moves in the correct direction.
The reason you only see sophisticated people doing this kind of trading is because you need a large and complex position with many hundreds of options to be in a truly market-neutral environment. You can't take advantage of mispricing without such a large position because buying/selling single options involves a tremendous amount of risk, so you need to do that as a part of a larger portfolio to spread that risk. Retail traders tend to spread the risk by doing 2 transactions (the mispriced option and a well-priced but mirrored hedge option), but that is a) much more expensive from a commissions standpoint and b) really limits the range of market-neutrality forcing you to adjust more frequently to stay market-neutral, again, with commission costs.
[ed: that's to say, you need a way to get more/accurate pricing information than reflected in the market - but for options, not assets]
If you buy put options for X at 10, and call options for X at 10, then if the price moves down you exercise the call option, and if the price goes up you exercise the put. Unless the price is totally fixed, you make some profit. The real question is whether this profit outweighs the price of both your options.
You need the price to move sufficiently for this plan to be worth it. Especially because in any case, either your put option or your call option is worthless. Thus, you need twice as large a price move as when buying only puts or calls. The upside is that you don't need to care about the direction of the movement.
The problem is that much more often than not the “only unprofitable move” is the one that happens. Options in general are too expensive and that’s why selling “insurance” is profitable most of the time. Maybe he can identify consistently mispriced vol, though.
This was the method I used, as described in another comment.