When playing the streams from tuner2.com, the vu in foobar is regually hitting absurdly high peaks (I saw a +7 briefly) - naturally it clicks like anything when this happens.

Its not in the source becuase turning the volume down to -5dB eliminates the noise and there is just the odd blip of red on the vu meter.

I want to know why this is happening.

It is in itself not so weird for HE-AAC data to have high peaks, but that it leads to audible problems is another issue.

Does the clicking go away when you lower the volume?

Yeah, they do, but then the HE-AAC streams are noticbly quieter then everything else that was played with the volume at 0dB in foobar, its not that the gain on the overall thing is too high, its just that its peaking at weird times, its not always when theres a lot of sound happening either. with the volume turned down, you see a peak come and almost hit 0dB, but there is no loud sound you would assosciate with a peak that high, like when bass hits or something, just a bunch of talking generally.

I can't tell you what's causing it, but applying the Advanced Limiter DSP might solve the audibility issue.