but given that Curie had little experience with commanding so many divisions at the same time, I'm skeptical this is true

Your scepticism is well warranted; like most of Lloyd-George's War Memoirs, it's bullshit pure and simple. Lloyd-George despised Haig, and went out of his way in the War Memoirs to torpedo his reputation. Currie and Monash were excellent corps commanders, excellent General Officers in general, but their status as among the most skilled commanders on the Western Front, when Lloyd-George was writing at a time when the idea that a Western Front General could have been 'skilled' was practically heresy, likely had more to do with this than any decision he may have taken in the war. Essentially, he pulled them out of thin air.

TL;DR: Nope; avoid the War Memoirs like the plague.

EDIT:

Robin Neillands shoots this down in his work on WWI generals; he even points out that Currie was greatly respected by Haig, and the feeling seems to have been mutual, Second Passchendaele aside:

"I met him many times, and although he never had much to say, he always impressed me greatly. Leaving on one side his manner, his bearing and his appearance – all of which fitted so well with his high rank, one felt that here you were dealing with a thoroughly honest, decent, manly man". - Arthur Currie on Douglas Haig