Thanks LittleMe Jewell. Looks like I just happened to have been selecting a few items where the "Get the demo version" link didn't work correctly, for whatever reason. I tried a number of other items that provided demos and they worked in that they then brought up the demo version page which normally lists a price of L$0 so I could put it in the cart and submit the order.
However, that still leaves the question as to why my friend could get a 'place your order button' but I couldn't for a certain item. Here's a link to it. This item does have a very adult sex image on it and so if you're offended by such images then don't bring it up. But I cannot get to the demo page for this Marketplace item - it simply brings me to the home page: https://marketplace.secondlife.com/p/Cheeky-HotBoy-Jeans-Blue-MUSCHI/5579619