Sort of. Yes the line is nylon and more specifically either a Nylon 6 or a 6/6 (has to do with the precursor chemicals used to make the polymer). These are both very common, high volume materials (read: cheap) and are also inherently very hygroscopic. That is true of many but not all nylons, but given the huge volumes of 6/6 in particular, if that is what you think of when you hear "nylon," odds are quite high you are right. Nylon has a lot of great properties, but moisture absorption can be a mixed bag as it can help in some situations and hurt a lot in others.
6/6 fully saturated holds about 6% water by volume, but fully saturated is not terribly common as it typically takes submersion for several days. But that looks to be what people are talking about here. Water in 6/6 acts very much like a plasticizer. Think of a vinyl 3-ring binder or document sleeve. This is PVC with a ton of plasticizers in it (often chemicals called phthalates) to make it flexible. PVC pipe is the same material but lacking those plasticizers so it is rigid. Well that is basically what water does to 6/6. That is why the line get less brittle and more flexible when soaked. It also greatly improves the impact strength of the material
But again, 6/6 loves water. It soaks it up from the atmosphere and will easily get up to a couple percent water in it in humid summer air. This is a bigger issue for those in very arid climates where the nylon can get quite dry.
This also shows up in injection molding. To mold nylon, you first have to dry all the moisture out of it, or it hurts the material properties. But freshly molded nylon parts can be sensitive to impact. This condition is called DAM (dry as molded) and is often listed on data sheets along with a couple other moisture levels (like 3% and fully saturated) to give you a feel for how moisture affects its properties. A coworker told a story from a previous job where they were molding nylon parts, putting a handful in a bag, sealing it up and shipping it and the customer was getting them already broken from shipping. He told them to put a teaspoon of water in the bag before sealing. No water was left in the bag when the customer got them but also no more breakage!
Probably more than you wanted to know (if you didn't fall asleep), but that is a summary of the science behind it.
Here's an example chart for Nylon 6, showing how it reduces tensile strength and modulus (makes it less stiff - aka softer) but also improves the Impact strength by a factor of 3 at the same time. It says in the website that this 50% RH air results in about 2% moisture.
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