A lot of people still wondering why they have issues with TF2C while using in-game Steam browser. Consider this as our official answer and spread this sacred knowledge among those who do not read this forum or just can't read at all.
We do not support Steam browser and will never do! This stripped down version of a browser was never designed to fully support comfortable Internet surfing. It doesn't support many contemporary technologies that TF2Center are using. So no complaints are accepted! Use it on your own risk and don't ask us to fix it.