My guess is the nails were made in China, they have a lot of "metals" over there to get rid of(they remove them from electronics-60 minutes I think it was did show on how the people that remove the metals died within 4 yrs of doing that kind of work.) so when you get anything, safety pins, nails etc it isn't quite up to US standreds. In other words, no telling what a nail has in it for metals, they stuck a lot of metals in kids jewelry too so they don't seem to care ! Safety pins buckle & I went through a whole box of them as they are so weak, some paint brushes made in China get rusty between the wood & bristles, nails often bend easier than American made, so I think it's mostly the nails & new home may of had a little moisture left in the wood when they built the house. We built a new gate couple of yrs ago & I had to touch up several times as seemed to shrink as wood dried. I'd try new nails as I don't supposed you have any 20 yr old nails. Doubt you have leak unless there is change in roof above the area like a valley not properly done. If roof is normal there(might check in attic & see if you see water stains, then you might need to check further.) I use roofing large head nails that are galvanized to hang things in our earthquake prone So. Ca. as the pics aren't nearly as likely to fall as they have to jump up to get off the nail.( They are longer nails about 1 1/4 in) Didn't lose a single pic. in last quake. If you repaint just dap a bit of bathroom caulk in the hole & paint over & no one knows.

I doubt China is putting lead and other metals into nails just to get rid of them because they are generally worth more than iron as scrap. BUT there is increasingly more scrap being used to make new products and the quality of steel can be degraded with contaminants, especially if you use the cheapest steel you can find where corners are cut in the production process to cut costs.

Also, many nails and screws and hardware bits are made here in the US because of the shipping weight issue.

I can see the studs in this wall being high in moisture when the house was built, but after a year it should have dried out. I'm a bit concerned about water leakage into the wall from somewhere.