Do you have a link to that article? I guarantee you, if someone is arguing that people were deep-sea fishing 40,000 years ago, it is solely based off of archaeological evidence of fishing gear, probably some type of bone or antler hook. With no writing from this period, and not even any depictions of human beings at all in art, artifacts are probably the only way that archaeologists would be able to guess about deep-sea fishing. I guess, unless there is some rock art clearly identified as a tuna or something, which seems very unlikely.

So if you have that article, it probably explains possible methods for fishing with whatever the artifacts were that they found.

Sue O'Connor and Jane Balme have a chapter in Southern Asia, Australia and the Search for Human Origins in which they say the following regarding the tuna fauna in Jeramalai shelter: "The small size of bones of pelagic species... indicates that mostly immature individuals were taken. As immature tuna sometimes come in close to shore, it is possible that they were caught by hook or spear from boats or even from the shore or reef edge". So it appears that the author cited in the popular article has reservations about the plausibility very early deep sea fishing. That's from a 2014 publication, so I would describe the conclusions in the 2011 popular science article as a tad sensational.

You might wanna ask /r/askanthropology. They could at least give you a run down of boat technology at that time.

"Deep Sea" fishing in modern times refers to being reasonably far offshore. The baits fishermen use are nearly always on the surface. Tuna can still be caught close to shore and is shallow water.

http://www.fishcrack.com/incredible-fishing-video-90-lb-yellowfin-tuna-free-gaffed-off-a-dock-in-islamorada-fl/

what do you mean by deep sea i know alot about the fishing of the northwestern Indians and how they fished for halibut,rock fish, and ling cod but im not sure if that would count as deep sea as it was at most a few hundred feet