The information about grades according to rank is correct if your considering you have no proper gear. I spent a very small amount of gil and got optimal gear for fishing. I am rank 13 and started fishing grade 3 around horizon with ease. Plenty of box turtles and black ghost. Averaging 270+ sp per catch.
I have to agree. Fishing is the only DoL you can rank up on higher grade nodes/places without limited gathering attempts.
I got my fishing up to ~R10 with some fishing in Limsa and leves in Skull Valley.
Then I got some gear to push my output and a R12 willow rod and went to the Isles of Umbra in western La Noscea.
The area is grade 10 fishing and although bite rates (with lugworms and blood worms) weren't that great, I had no problem getting my rank up to 16 in a few hours.
It's been some time but SP gain was around 600 per catch if I remember correctly.
The only problem can be the Snippers/Clippers there if you fish from the paths in the cliffs at 4,20/5,20.
Don't waste your time fishing low grade places for 100SP per catch if you just want to rank up.
With good gear and high output for faster bites you can gain at least 2-3 times more SP without seeing a big difference in bite rates.
Just make sure to use the right bait or lure and don't just stick with the R1 NPC bought worms and bugs.