Clinically/academically, you're right about transsexual vs. transgender.
You can be right, and still lose, though.
Use [Google blog search (beta)] to look up Transgender. There are 461,684 page hits. Most of them are about trans rights, and transition, and where do I get hormones/counseling/etc.
Now search transsexual. 380,343 page hits, with words like horny, slut, fetish, and a lot, lot worse.
I'm a DES son. Mom went to medical school, we always had a PDR in the house. I'm post-op. I transitioned on the job and still work there. I'm not a horny slutty [____] (etc, etc, etc,) but a valued employee.
In a perfect world, transsexual and transgender would mean what you say they mean. But they don't yet, and they won't for a while. Meanwhile, to those co-workers for whom my transition is still a big deal, I'm 'transgender', because it ain't got nuthin' ta' do with SEX.
If that's' what it takes to keep the peace in my little corner of the cosmos...