<font color=navy>I don't see anything wrong with it, as long as they let you know up front how much it would cost.
My perspective is that if I'm going on a trip, can't afford to pay for one of my kid's friends to go, but want to give them the opportunity to join us, then I offer the opportunity to the parents. It's their choice whether or not they want their child to gain that experience.
We usually invite one of the kid's friends to go on camping trips with us. I like to invite kids who wouldn't have that opportunity otherwise. I let the parents know what the extra costs are - horseback riding, kayaking, etc. We've taken three kids with us, so far, and their parents were more than happy for their children to join us -- they got to do something that they wouldn't have been able to otherwise (their parents don't do that stuff). Everytime has been a positive experience. (We go to Sequoia & Yosemite). If I had the money I would pay for it, but, frankly I don't. My opinion is that at least we're giving someone a chance to do something. The parents also offered to pay for food, etc., but I told them I had that covered, and not to worry about it.
If someone invited my kids to go somewhere, I would expect to cover my own children's expenses.