Is this actually close enough to true, though (even if the "99%" is taken to be figurative), even after all the media coverage?

There are two trends that would lead me to think that this estimate is too high (by a margin large enough to matter). Firstly, the degree of gender dysphoria in the median trans individual is liable to be decreasing at the same time as the number of trans-identifying people increases--for instance, in the Netherlands, the fraction of people entering the gender identity center who start hormone therapy has dropped from ~90% to ~65% while the overall numbers have increased twenty-fold. This is perfectly natural for a society with trends of decreasing stigma against trans people, and increasing awareness of trans people and gender dysphoria. However, this also means that gender dysphoria is likely to be a less central and defining characteristic for contemporary trans people than it was historically.

Secondly, trans people consume media too, and given humans' powerful coalition-building instincts, if you hear that your side's position is such-and-so, you're more likely to adopt such-and-so as your own position. So as the media focuses on more extreme rhetoric, it is liable to lead to a skewing of views to greater extremes--and there's no particular reason to believe that this effect would be any different in trans people than elsewhere. As a personal anecdote, one trans person I know (from tech circles) was attacking people quite vociferously (with the you-have-to-do-this-because-we're-just-trying-to-survive style rhetoric, which can reflect reality but doesn't always) because they were supporting someone who wouldn't cancel someone who (once) wouldn't cancel someone who had hostile and intolerant right-wing-ish beliefs (that they weren't expressing at that venue). This sort of transitive existential threat makes perfect sense under the model of the most vocal postmodern trans advocates, but otherwise is kind of hard to explain. (This was before the most recent intensifying of the strident conservative anti-trans rhetoric, so it's not explicable as a reaction to that.)

So I think you might be mischaracterizing the degree of support for different outlooks. A loud 1% backed by nobody is a lot easier to deal with than a loud 1% backed by, say, 20%. (This doesn't say anything about what approach is wise, just about how hard it might be to change direction or discourse.)