Yes, meta absolutely is different from main sites with respect to comment usage. It's not a "double standard", they're just different situations.
One of the primary purposes of meta is discussion, and its audience is site members. This is even official: all meta posts require one of a handful of tags, and one of those choices is discussion. It's totally natural for meta to end up involving a fair bit of discussion in comments. Those comments don't really cause much trouble if left around, and can even be useful for future users who want to see all the various details of everyone's thoughts. It's also simply not that formal. When the whole audience is site users, chattiness among site users is no big deal.
On the other hand, on the main site, the audience is... everyone. The aim is to create things that are useful for future readers, including those coming in from search engines. The page needs to be useful and concise, for people who just want an answer to a question, not a bunch of side discussions between people they don't know.
That means that comments on the main site really should be focused on improving the posts they're on. That means suggesting improvements, requesting clarification, and so on. The exact implementation of this general idea does vary from site to site, largely because some sites are prone to really large comment discussions, so they try to shut things down quickly, while other sites don't have as many issues, so they tolerate a bit. (On top of that, implementation of policies may be uneven - it relies on flagging and moderator action, so some things get noticed and addressed, while others don't.) If you see this being enforced fairly strictly, that doesn't mean it's religion, it's just the community and its mods doing their best to flag and handle comment discussions to keep the questions/answers useful for future readers.
On top of all of this, in many cases, main-site comments that aren't suggesting improvements or asking for clarification often aren't actually helping arrive at good conclusions. If things are turning into generall chattiness or heated debates or tangential discussions, that's not building consensus. This is why you'll often see suggestions to simply write a different answer if you disagree.
Finally, I would note that meta is not completely removed from these rules. If things do get excessively chatty (or heated or tangential) mods will often step in just as they would on the main site. But things can go a bit farther before they're too chatty/tangential than they could on the main site.
As for sources for meta being more flexible... well, I would really try to look at this as more of a description, and an absence of a policy for strict enforcement. This is simply how things tend to work on meta. It is that way because no one's ever seen much reason to try to change it significantly. The fact that you can't find meta posts saying "I think we need to crack down on comments on meta!" is the proof.
If you want something "official", there's a note on tone in one of the answers to the general Meta FAQ, which is in turn linked from the main FAQ:
Meta has a reputation for being more... relaxed than the other Stack Exchange sites. Jokes and non-serious posts that would be swiftly deleted on the other sites have been welcomed here in the past and are sometimes still tolerated today, though not to the degree that they were before.
But again, that's more of a convenient short description of how meta works than an absolute statement of policy.