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Is there a reason why it's considered ok to put a 23mm tire on a 23mm rim but unsafe to put a 32mm tire on a 31mm rim?
Internal width is the critical dimension. As rims get wider, the internal width is a greater proportion of external width. In your example, assuming the hook accounts for 3mm per side in both cases, the ratio of internal width is 17/23=0.74 in the first case and 25/32=0.78 in the second. It's a marginal difference, and there isn't really a hard cut-off, but >0.75 is something you want to approach with caution, just as <0.5 is. I have run at 0.84 and 0.41 without succumbing to fiery death, but in both cases I'd have been better off closer to the mid range. All of the above relates to road tyres. For MTB tyres, the manufacturer will usually have designed around lower ratio, probably somewhere between 0.3 and 0.6
I'm assuming that @Kyslo means a 19mm external width, i.e. 13-15mm internal, in which case Sheldon thinks either don't do it or it's at the extreme end of the viable range. We've all learned a lot about tyre/rim interaction since Sheldon died, and I think most people would shift his table by at least one row to make wider rims the preferred choice.
I did this tweak some years ago: