Historically, this was shortly after Intel lost the battle to trademark 80486 and 486, and thus began naming their chips, Pentium, for the fifth generation 586 chip. Along with that they had a huge PR campaign about how much higher quality the Pentium was, compared to "generic" 586s.
It was in that context that the Pentium floating-point division bug appeared. In the context of the new branding and the "quality counts" PR campaign that went along with it, that bug had the potential to not only undo the effect of Intel's "quality counts" campaign, but flip it on its head into an even bigger negative than was the positive they /had/ been trying to get. Intel wasn't undone so much by the bug itself, as by the whole quality counts campaign they had been running.
In that context, once the bug went public, Intel really had only one choice, make good on the quality counts campaign and fix the problem. Had they failed to do so, Intel and AMD could be in reversed positions today, because AMD would have been the direct beneficiary. But by doing the recall and making people who had the defective chips whole even at huge cost, they did far more than a few ads in a "quality counts" campaign could have ever done, thus solidifying their place in the public mind as a quality vendor that stood by their products, thereby securing their dominance at a critical juncture in the desktop computing market, then and for another decade.
So yes, public demand did have a bit to do with it, but the far stronger force was the effect of their own advertising campaign at the time, and their ultimately correct call to reinforce instead of negating that, thus ensuring their dominance for a decade to come. Had their ad campaign been about something else, or had the problem happened with 486 or 686s instead of 586/Pentiums during and immediately after this campaign, they may indeed have been able to successfully shove the bug under the carpet and continue as if it had never occurred, and they very well might have done exactly that.
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