Ideally, the H1 tag will explain what the page is about, an action the visitor should take, the value the page provides, the question the page addresses, ETC.
Mirroring the page title as the H1 on a form or conversion page isn't a very good idea either, even if the page has no bearing on your SEO.
As an example, look at the phrase: "Organization" TV Commercial: Join "Organization"
where "Organization" represents a name, like "Red Cross", Insane Clown Posse", "Young Democrats", or "PETA"
I think you would agree that it's a pretty awful header on a donation form that you drive direct traffic to via TV commercials. This phrase makes more sense as the title of the page, but not as your page header.
