If it is true then, from which gen did it started and by how much does it increase?
Okay, so I did some research. In Kalos Route 16 a fisherman in the fisher shack gives you a Super Rod and says that consecutive fishing can increase the chance of a rarer Pokemon (Yes thats not waht you asked but he also says something bout being in an enclosed area! And using the ability Suction Cups and fishing in an enclosed area increases the chance of fishing a Pokemon. This is most likely introduced in Gen 6. I couldn't get any info for this in other gens.