I dug around the workshop today and as it happened I had a Soundcraft power amp board. I have also been trying to fix my Hameg function generator, but as Hameg refused to supply the schematics and asked for a repair fee considerably more than the market value of the machine, I had it enough and decided to part it all out. So, I have a pretty good case example there too.
Below is from a Soundcraft power amp. The resistor leads are bent. Have a look at the pad size and come to your own conclusion what electrical or mechanical benefit can exist by bending the lead in that size of pad area. May be in radio frequencies? I do not think so. I will come to that later on.
However, as I mentioned before, for speed of assembly it makes sense and in this case since there is generous component spacing it is reasonable to think that it is safe. But see the areas circled in yellow. See how close the leads are, particularly in the first circle. And try that in a densely populated board. Major risk.
The below picture is from the same board. Power resistor and its solder node. It is not bent. So, if there was a gain to be made from mechanical strength and heat dissipation point of view, this is where you want the lead bending to be. So the argument again does not hold.
Next pictures below are from my now RIP Hameg. The entire board is through hole components and leads soldered straight.
The picture on the left is the output stage where the BNC is connected to the board through the yellow wire at the bottom of the picture. The picture on the right show the solder side. Now, again if there was any electrical benefit such as reduction in resistance due to long component lead from bending, this is where you want it to be the most. That area handles 10MHz. The people who design these equipment surely know a thing or two. But they chose not to, because longer the lead greater the inductance and you certainly do not want anything like that here. So, again there is no electrical benefit in bending.
In summary, bending the leads provides speed of assembly where it is safe to do so. But that's all. The claim that it must be done that way, or it is the correct way of doing it is not correct. I also argue against the claim that it provides superior electrical performance. There is no evidence of that.