Tannin is a common name for something like 'liquid extracts from plant material'. They can be both good and bad, depending on the origin and the concentration. The tannins from oak leaves and bark can be used to preserve leather, tannins from coffee give it the dark color and can work as an insecticide but also as a weed killer. Phenols from pomegranate have shown to be degraded by our gut flora into compounds that seem to have a positive effect on mitochondria, extending their lifecycle. It's still a matter of investigation though.
In general, I think that tannins from fresh material could have negative effects. The carbon molecules (mostly phenols and/or aromatic compounds) inside them are usually signalling molecules that tell surrounding plants and surrounding microbes that a tree is injured or dying. Phenols are short lived though, and they oxidize pretty fast.
So if the bark is cured/dried for a couple weeks or months, then most of the negative materials have been broken down. Of course, the bark on the outside of trees has been washed by the rain multiple times and exposed to sunlight and air for so long that I think the curing isn't even necessary.
If the bark is sterilized or pasteurized, which is the case in most pet store bark, most of those aromatic compounds are long gone. I ruined an autoclave once by trying to autoclave pine wood; the insides of the steam vessel were covered in dark sticky material that smelled like barbecue. I know for a fact that the smokey flavor in hotdogs and other food products comes from stuff like that (over here known as 'smoke extract'). It can be highly flammable and even explosive if it contains too much nitrogen, which happens when fresh wood is used.
I believe bark in a bag is sufficiently cured and dried to use in our soil. If the negative effects would be big enough to notice, I think we would've heard more about it.
In the case of growing orchids, where seeds need to be inoculated with bacteria and fungi (from the mother plant) to germinate and live, I can see why the bark needs to be treated; seeds don't germinate well in the presence of some aromatic compounds and if the tannins have an antibacterial or antifungal function, then the inoculation could not be successful. Orchid seeds don't store starches and sugars like most other seeds, so orchids actually rely on symbiotic fungi to give them a chance at life. If those fungi can't live due to the tannins, then the seeds can't live either. In the case of germinating orchids, I think it's a good idea to treat the bark if it's not treated already. Most plants that life in forests however, can deal with pretty high amounts of tannins. Just have a look at the water color of the Amazon river; it's mostly tannins, and life thrives over there.
