Basses take about a year (one full seasonal cycle) to settle into position, as the materials will compress in some areas and decompress in others under the strain of having strings on under full tension. The weight of the tension is roughly equal to an average-sized man, so it's a pretty hefty force and wood just isn't accustomed to it when cut fresh from the tree.
Hence, the first few months of any guitar's life will involve a number of truss rod adjustments. Some guitar's necks will always move a bit, even once broken in.
Regarding strings, I do notice that they stiffen up with age, IF not played regularly. I've also noticed that Rotosounds are particularly succeptible to this. However, if you play them at least once every 2-3 days, they stay pretty loose and yes, maybe even loosen up more over time. My current set are three months old, heavily played in, and feel dull and stiff if I leave them for a few days with no attention. But as soon as I start bashing away on them again, they start softening up and even sounding a bit brighter.
I have to say though, Rotosounds DO exhibit this more than D'Addarios (the only other brand of string I've used for a long time), which leads me to believe that they're engineered slightly more towards people who play their instruments very regularly, and very hard (look at the list of endorsees: Billy Sheehan, Geddy Lee, Steve Harris...). They're definitely tough as nails, so it'd make sense.
I don't see how old, stiff strings would pull harder on the neck though (and thus cause a flat neck with lower strings), because the tension/weight force won't change. "Stiff" just means they won't flex so easily.