Apparently, the story intimates that 5 d4 was so ubiquitous in the Petroff of the day that Alapin did not even think of the possibility of Tarrasch playing anything different, and so reached for the Bishop.

He also apparently did realize before actually moving the Bishop that Tarrasch had indeed only moved the Pawn one square, but as I noted previously because of the touch-move rule, there was nothing he could do for it, because legally he was required to play 5 ... Be7 for better or for worse.

As for the alleged ubiquity of 5 d4 at the time, even a master could be forgiven not knowing about fairly obscure games like Von Der Lasa vs Jaenisch, 1842 (for which we still don't even know enough details to fill in some ? marks in the database!); however, a look on CG shows that the single step was essayed at at least one relatively high profile event, the tournament in London in 1862 (F Young vs Hannah, 1862 for instance). Even in the pre-internet days, I would expect that a master would peruse the tournament records of at least the better-known events of the time ...

The most likely explanation, however, is logistical. I'm not sure what rules were in effect in different locations in the 1880s, but in those days, the rules of chess were still evolving (outside of the very basic rules of the movement of the pieces etc. that define the game of Western Chess as such) and much more subject to change than they are in today's chess world. For instance, the use of clocks wasn't standard until some time during the second half of the 19th century, and even such a basic rule as the threefold repetition draw claim hadn't solidified until at least the late 1800s either. Moreover, as there was no central chess authority in the pre-FIDE days (outside of what major organizers like the London Chess Club ruled for their tournaments) the more "administrative" rules (which touch move certainly qualifies as) could be expected to vary slightly from year to year or even locale to locale.