I owe this thread a huge thank-you...
I had two betta leaf hammocks in my tank...one had the wire and one didn't, the one with the wire was starting to rust and I hadn't even noticed it. I threw it out. Who knows what harm that could have done.
I also had the plant on the left:
I took out the wire just now. Wasn't rusted, thank goodness. I put the plant back together just fine without it, which leaves me to wonder...why do these companies even bother to use wire when the plant works just fine without it?
unless your betta is a huge monster and insists on ramming into it, the plant doesn't need a wire in it to stay stable.
Now after reading this thread, I'm really worried about two of the new decorations I bought for Flareon...the pink trees here. I haven't noticed anything yet, and the stems of the flowers(?) don't have any wire, and Flareon seems to like swimming on top of them and his fins look fine...but I guess I will have to check for any paint peeling.