I guess there wasn't much they could have done, except for letting it burn in a half way controlled manner.
Those barrels hold about 150 ltrs each - so 45,000 barrels is roughly 6.8 mio (!) ltrs of booze. Usually Whiskey has 42% alcohol, so we are talking about close to 3 mio ltrs - or 3000 tons - of pure alcohol. If that has reached a certain temperature, nothing in the world puts that fire out.
And if they would try to wash it away with lots of water, it end up in some river . I don't think the fish will appreciate the free drinks.

Yes, I've seen that How its Made show as well, quiete interesting to see the production even of everyday things. Usually we don't really think about how some stuff is made, and in which incredible amounts its made.
Other trades have nearly died out. There is probably less than a dozen people in Germany who still make saddles. Or baskets out of willow twiggs. It used to be thousands of people in the old days, but today nobody can pay the labour cost anymore. A decent saddle made in Germany costs about 4000 Euro, they said.