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I think your answer is a good conventional one, but I can't let it pass without comment. Polyamory is a lifestyle in which people accept that you can be honestly in love with more than one person at a time, be open with all parties about it and enhance the life and love of everyone involved. I've experienced this myself and a googling polyamory will provide many resources, such as http://www.polyamory.org.
Polyamory is not really about sex, like swinging. It is about romantic love for more than one adult simultaneously.
We've all been raised with the idea that romantic love is a limited quantity, so any that you give to one person cannot be given to another. I think that is dead wrong. Just as you can love more than one child without diminishing the love for any, loving more than one adult does not diminish the love for each.
Of course since none of the people involved are likely to have even heard the term, let alone thought that it made sense, just blithely saying "it looks like you're polyamorous" doesn't really solve the problem. But after going though the good points you made -- I particularly like noting the shock of misunderstanding the nature of the relationship -- it seems to me that it would be worth at least mentioning polyamory.
-Steve