No, he is correct. There are two types of inflation, monetary inflation and price inflation. Your parent is clearly talking about the latter. This is the standard definition of the term inflation (look at the titles of the wikipedia articles there).
By that definition, bitcoin should be measured against what it can buy, or the real value of bitcoins. However, few things can be bought directly with bitcoins, and even some of those things might automatically fluctuate with the value of bitcoins in USD. So when bitcoin fluctuates against the dollar, that is indeed inflation/deflation due to what can be bought. You can substitute USD for CAD, AUD, or Euro as you prefer, that is just the only way to buy most of the goods on any reasonable price index. Your comparison with imports/exports is mistaken.
If bitcoin was adopted by a country, most of these problems would disappear, at least for those living in that country anyways. Since you must tie bitcoin to any other currency at the moment in order to buy necessary goods, let us use the fiction I'll call "Euro-Bitcoin", which is bitcoin as tied to the euro currency, instead of giving bitcoin a country of its own (which would change the current situation considerably). You will notice some bonus deflation in Euro-Bitcoin should the euro decrease relative to bitcoin, and some bonus inflation in Euro-Bitcoin should the euro rise relative to bitcoin, or should the market decide to raise the prices of common goods (which can happen completely separately from monetary inflation). This will be negligible for our discussion, as that plagues all currencies, not just bitcoin.
Now, the fact that you cannot just buy milk at the local grocery store using bitcoin creates another problem for Euro-Bitcoin. This is that someone must be willing to exchange bitcoin for euros in order for your Euro-Bitcoin value to be spendable. Now, the price at which someone is willing to exchange your bitcoins depends on the perceived demand for bitcoins in the market. If people want to own 10x as many bitcoins, the price of bitcoins jacks up, and the value of Euro-Bitcoin increases. If the reverse happens, the price of bitcoins plummets and the value of Euro-Bitcoin decreases. This is the inflation which the GP was talking about, the purchasing power of the bitcoin, with respect to buying real goods, can decrease or increase significantly according to bitcoin demand.
Right now, should any one major holder of bitcoins get rid of a significant portion of their bitcoins for the euro, it is conceivable that would saturate the market for bitcoins and decrease demand. This could cause the price of bitcoins to drop fantastically, since there are only so many people trying to buy, say, several hundred thousand euros worth of bitcoins. Bear in mind that since most bitcoins are being held, rather than being used, in general the pool of bitcoins available for exchange is much smaller, so the whole bitcoin economy must fit inside a fraction of the total Euro-Bitcoin value of bitcoins in existence. Should any significant fraction of that value be suddenly put up for exchange, that will tank the price. That may or may not happen, but if it does, it will mean inflation, lots of inflation.
I think it is also reasonable for the price of bitcoin to drop gradually, which also creates significant inflation (by definition), but that won't kill bitcoin, only decrease the value of everyone's bitcoin.
Personally, I don't like the "rich get richer" nature of (monetary) deflationary currencies, but bitcoin can suffer from inflation under the wrong circumstances.