It's not just the DHT22's accuracy that's a problem, it's the calibration.

I have 8 of these, and they are up to 30%RH off - both in terms of their readings relative to each other, and relative to the true RH of a saturated salt solution[1]. Moreover, some of them have a strange "stickiness" to certain levels.

I've heard good things about the BME280, and that's what I intend to replace my DHTs with.

[1] See e.g. http://www.omega.com/temperature/Z/pdf/z103.pdf