A version of Taler that didn't allow auditability wouldn't fit the description on its website, correct. That has nothing to do with whether or not it's a "backdoor", and more importantly, it has nothing to do with whether or not it's a desirable part of the functionality, regardless of whether or not you want to call it a backdoor.
Again, we can say the same about Bitcoin. I think you're being disingenuous in implying that a non-backdoored version of Bitcoin wouldn't allow double-spending. Theoretically Monero might fit the bill, but given that neither Bitcoin nor Ethereum have adopted Monero's transaction model, it's pretty obvious that the maintainers/community don't view plugging that hole as a priority.
> Auditing of the validity of the transactions that doesn't require exposing private information to third parties
> Auditing by everyone, not a select few with privileged backdoor access.
This is an interesting criticism, because Bitcoin objectively exposes more information to 3rd parties than Taler does. What you're arguing to me is that Bitcoin is more private because it exposes my information to literally everyone, and not to a limited subset of people.
It's like saying that my banking balance isn't private because the bank can check it, but if the bank instead broadcasts all of that same information to all of my employers and anyone who asks, then it's suddenly OK. It's like saying that if my partner has access to my phone that's a backdoor, but if instead Google just lists all of my contacts publicly on a webpage, then it's not a backdoor anymore. It doesn't make any sense, things become more private the fewer people who have access to them.