I think (but am not confident) I have a better sense of what's going on. That is, I wondered why I was seeing a crash message for iexplore.exe, even though I could continue browsing just fine.
From reading through this MSDN blog, it makes more sense now: http://blogs.msdn.com/b/askie/archive/2009/03/09/opening-a-new-tab-may-launch-a-new-process-with-internet-explorer-8-0.aspx
By default, IE 8 will spawn 2 instances of iexplore.exe. 1 instance for the frame (where the HTML renders) and 1 instance for the tab. Given I cannot do anything with tabs, it must be this second instance being used for the tab that's crashing.
I wonder what'll happen if TabProcGrowth = 1 instead of = 0, as originally suggested at WineHQ? I may not get time to test this for a little while, if anyone else does, please post your findings. I'm especially interested to know if it eliminates the extra iexplore.exe process from crashing. Per the blog...
TabProcGrowth =0: tabs and frames run within the same process; frames are not unified across MIC levels.
TabProcGrowth =1: all tabs for a given frame process run in a single tab process for a given MIC level.