A long, long time ago I was taught that TIR was Total Indicated Runout. So I Googled total indicated runout and found my memory is maybe correct. Sometimes google is handy to get variety of explanations/opinions in different references. I think the Total Indicated Runout interpretation is preferable because it resolves the oval shaft conundrum.
And the different interpretations remind me of the DNC for Distributed Numerical Control and DNC for Direct Numerical Control discussion.
An open mind is a virtue...so long as all the common sense has not leaked out.