I think their rejecting Daniel's being taken in 624 (Daniel getting too old?) is an additional argument that derives from the other considerations outlined in the WT, Studies and Pyramids publications. It doesn't look like it's one of the original reasons for rejecting any captivity in Neb's accession year.
Summarizing their arguments:
1. It is a mistake to count the '70 years' as 'captivity.' It should be '70 years desolation.' This means counting anything from Jehoiakim's 3rd year is a red herring.
2. '70 years desolation' implies 'without an inhabitant.' That only happened after Zedekiah.
3. Because the plain reading of Dan. 1:1 and 2:1 throws a wrench in the works of their nice, 'harmonious' biblical chronology, as well as the apparent '3 year training' discrepancy, they must be doubtful readings or be understood differently. So 1:1 must really be referring to 3rd year of vassalage to Neb, and the '2' in 2:1 should be corrected to year '12' of Neb.*
I think that's pretty much the extent of their argument here. I can't see any more objections to Daniel being taken in Jehoiakim's 3rd year.
*Pyramids refers to the Varorium Bible. A search eventually led me to The Sacred Books of the Old Testament; a critical edition of the Hebrew text printed in colors, with notes prepared by eminent Biblical scholars of Europe and America (1893), Vol. 18 which, on p. 15 (please note the book starts back-to-front in true Hebrew style), says one should assume a "transcriptional error" and insert a '10' after the '2.' According to Jonsson's research (GTR4, p.337, n.60), the '12' suggestion is an old idea based on a LXX variant.