> maybe they've just got better over time at not relying on cookies for things they shouldn't?
It may be that. I just tried and Twitter is working perfectly without third-party cookies. Some months ago it didn't allow me to login.
With Google I had a similar problem, I couldn't login into my Google Account in sites that weren't the search engine (Docs, YouTube, etc). I just tried them, and again, it seems that it works now.
I use Chrome stable. Maybe something changed in the management of third-party cookies in recent releases?