To be perfectly clear, underscores have always been allowed in DNS since the very beginning. RFC 1034 has this to say about the syntax of labels:
3.5. Preferred name syntax
The DNS specifications attempt to be as general as possible in the rules
for constructing domain names. The idea is that the name of any
existing object can be expressed as a domain name with minimal changes.
However, when assigning a domain name for an object, the prudent user
will select a name which satisfies both the rules of the domain system
and any existing rules for the object, whether these rules are published
or implied by existing programs.
That means: if you put hostnames in the DNS, restrict yourself to the rules for host names. If you put mail domains, restrict yourself to the rules of RFC 822 If you put DKIM or ENUM records in the DNS (which are not hostnames), restrict yourself to the syntax of those protocols. If you put something else, follow the appropriate syntax. But DNS itself will not constrain you.
RFC 1034 goes on to make a conservation suggestion on syntax which specifies labels without underscores. But this is only a suggestion. It says "The following syntax will result in fewer problems".
So for sure GoDaddy is wrong to deny you "this_bites.com". Even if underscores were categorically disallowed in host names, you might want to fill this domain with DNS names that represent something other than host names. DNS registrars and nameservice providers shouldn't disallow that!
The next question is, are underscores allowed in actual host names?
RFC 1034 says about host names that "the old rules for HOSTS.TXT should be followed". But if the rules for HOSTS.TXT were old when RFC 1034 was written, they're ancient history now! RFC 1034 was written as a time when usernames commonly couldn't exceed 8 characters and everything was ASCII. The world has changed.
I would say that there is no single set of rules that define what is a valid host name. It just depends on what the software in use supports as characters that may be part of hostnames it uses for systems to designate themselves and peers. By "software" I mean all of the pieces of software that deal with hostnames in one way or another, from the operating system through network monitoring agents and everything in between.
If you are reasonably sure that there is nothing in your environment that would choke on a hostname that contained an underscore (and I think that, these days, that's a pretty good assumption), then I think you're safe to use them.
If there is something stopping you from using underscores in host names, though, it's not DNS, and never was.