Below is my understanding, although I find the statement inaccurate on some points and borderline wrong on others.
If you have bought an option contract, your payoff is $(S-K)^+\geq0$ where $S$ is your underlying and $K$ the strike. Therefore you can only receive a positive cash flow: there is "no downside". I guess he means that, because you can only get a positive payoff, it matters less whether you got it right when modelling the option price: anyway, you can't lose money once you've paid the premium.
By "variation comes from the upside", I guess he means that, the more in-the-money an option is (so for a call option, the more $S$ is above $K$), the more your delta is closer to 1. So the variation in (absolute) value from your option is greater the greater you are in-the-money. On the other hand, depending on how out-the-money your option is, then a change in the underlying won't really have much impact on the option value. So: when you're losing, modelling risk accurately is not necessary because anyway the variation in the option value is low; and when the variation is large, it doesn't matter that much either because anyway you're in a winning situation.
"The process used for modelling the underlying index cannot become non-positive": I don't know what that means. That's only true for options on positive processes obviously, such as a stock or an equity index, but not true for a caplet on a LIBOR rate for example, which can be modeled with stochastic processes that might take negative values. I have no clue as to why he thinks that generates asymmetric model risk.
That statement ignores a few facts:
- It does not account for counterparty risk. It is correct that, once you've paid the option premium to your counterparty (e.g. an investment bank), then you can only receive a positive cash flow, but the party that sold the option to you might default and not be able to pay you back the option payoff: that is what CVA prices, and it is important to model it right, otherwise if your counterparties do default you're in for nasty surprises.
- It also seems to ignore mark-to-market accounting rules: even if you hold a call option which can only pay a positive cash flow at maturity, in the meantime you hold that option in your balance sheet. The underlying value $S$ can vary; this will make the value of your option vary; and this will be reflected in your balance sheet and income statement. I think it's pretty important to have an accurate model to represent those values.