What is safe for birds or mammals does not necessarily mean it is safe for amphibians. Frogs, toads, newts, and salamanders are especially sensitive to compounds called phenols, which are present in many types of wood. Other types of wood, like walnut, are outright toxic as an evolutionary measure.
While in the wild this is generally not an issue, in an enclosed environment like where we keep our pets, these chemical compounds can build up to dangerously toxic levels. In the case of Osage orange, the risk of a food insect becoming contaminated and then eaten is very high.
The list of "safe wood" is by no means all inclusive, however the wood listed there is all proven safe for use with amphibians. You should not worry about wood rotting away in your enclosure. One properly sterilized and dried, the wood will outlast the life of the enclosure (and often the pets too).
As Kurt stated, "When in doubt, leave it out."
A bit of work with a Dremel tool and some PVC pipe will solve all your fears though. Have a search for "PVC" here on the forums and you will see the results of such a project.