Correct.
That is why i recommend you focus on your favorite weapons. By levelling as many perks up as you can you will have a stronger weapon that much faster instead of just levelling up every weapon. When you are just running straight to the next biome all the time, not only will your be very under-levelled but you never spent the time/effort to level up the perks.
Also use the alt-fire modes as often as possible. That is the only to level it up.. by using them.
Obviously you cannot control what weapons you get throughout your run.. Or can you?
Controlling weapon drops:
I believe this is still in effect. If you do not pick a weapon, it will not be added to the pool of available weapons for that run and you will never get it again once you move on the next biome. The theory is this. You always start with the pistol. Let's say you want to focus levelling up the Hollowseeker and the Electropylon driver. And as luck would have it the first weapon you find is a Hollowseeker. You pick it up and fire/use it. The next weapon you find is the Spitmaw Blaster. Do NOT pick it up. Nor any other weapon you do not want. If you make it to Biome 2 with the Hollowseeker (picking up other Hollowseekers is okay), then the Spitmaw Blaster and any other weapon you skipped will not drop again throughout your run. Also if you have a very powerful Hollowseeker and the Electropylon drops, even if you do not want to swap to it, because it is one of your favorites, you should pick it up, fire it a few times and then swap back to the Hollowseeker. Then you guarantee that you will get either the Hollowseeker or the Electropylon later in the run.
I've never cared for controlling my drops since i've use all of them and have long since levelled all the perks to max but this trick will help you focus on certain weapons.