I researched these hammocks, too. I found what you did: that while bettas love them, they can be injured or killed by the wire that runs through it. Even if the wire isn't sticking out, it could become so over time.
A member here had one kill her fish - the wire gutted it. No joke, scary stuff :(
However, where there's a will, there's a way! Especially if aquarium sealant is involved. I used it to "baby proof" my hammock as it were. Basically I gooed it over the vein on the underside where the wire is and anywhere else that had the remotest chance of wearing through.
For good measure I also used sealant to attach the leaf to the cup because I read it had an annoying habit of falling out.
After the sealant cured, I gave the whole thing a good rinse and stuck it in Flambé's tank.
Well let me tell you, he LOVES the thing. He likes to rest on the stem where it meets the suction cup (good thing I glued it!). He also likes swimming around it. I caught him doing a double loop de loop around it the other day
Anyways, while I'm fairly confident that I've made the leaf as safe as I can, I'm still checking it every water change to make sure the sealant is holding up.
EDIT: Of course you can always make your own wire-free hammock with aquarium sealant, suction cup and an aquarium safe silk leaf. I had the sealant on hand and the hammock was on sale so that's why I spent the time I did on it.