Personal experience reading filings. In most states (and certainly in California), there's no need to prove any particular or even general allegation in a filing. It's basically a license to rant about your soon-to-be ex. Most people aren't dumb enough to pay lawyers extra to spout off; they just want the divorce. But as you can imagine, giving people who are hurt, bitter, and angry about a failed relationship a venue to publicly berate their partner does often enough lead to all manner of nastiness. This isn't new, either; it's been going on for as long as there's been divorce. It makes for mildly entertaining reading, but one can't really take any of it as fact.

Civil filings in general [0] have no required proof: they are simply the places where the contentions which will be at issue later in the process (where they generally will need to be proven) are laid out. This is just the basics of the legal process and what a filing is by definition; they precede and frame the part of the process in which proof is involved.

[0] Criminal filings are somewhat more complex, and differ between cases proceeding on indictment vs. those on information.