You've got it backwards. Never trust a font to provide your kerning, always adjust. Proper kerning is a fundamental tenant of good typography. Designers have always and will always manually adjust kerning.
Yes there are times, especially with display type, that you want to adjust the kerning between a few pairs of glyphs, but to say to "never trust a font to provide your kerning" suggests to me that you use a lot of poorly designed free fonts rather than professionally realized typefaces from reputable font foundries.
I would love it if the browsers would all support the built in kerning in a font by default, with a way to override it manually.
If you are using quality fonts, as you should be, you will only need to adjust the kerning in very rare cases. The type designers are the ones who have to concern themselves heavily with the font kerning. Which is why font design software, such as fontlab or glyphs, have an insane amount of kerning related functionality, whereas the kerning provided by something like, say, photoshop or indesign, will do what you need it to--which is make minimal adjustments in corner cases.
And print designers do have access to high-quality fonts.