For the most part, the hydraulic portion of the braking system is air-tight when in good working order. The cap on the reservoir creates a seal, and then has flexibility to allow the amount of fluid in the reservoir to decrease over time without breaking the air-tight seal.
NOTE: The reason it needs to be able to do this is so as the brake pads wear on a disk/rotor setup, the caliper piston extends outward towards the rotor and stays there. The extra fluid needs to be given to the caliper to still be able to apply braking force.
While the hydraulic portion of the braking system is basically air-tight, it isn't completely air-tight. You aren't taking into consideration that the rubber or soft components of the system, such as brake lines and even the cap seal of the reservoir, are air permeable. This can allow air/moisture into the fluid. Mind you, it isn't a lot of moisture, but it adds up over time. Even if you had something on the cap to remove the air or replace it with something else, moisture ladened air will still be absorbed through the other soft parts of the braking system and the fluid will still become contaminated over time.
You may ask, "Why do we even use 'soft parts' in the first place if they will allow moisture to be absorbed?" It's a tradeoff. If you made every part out of material which is non-permeable, the system would self destruct because it wouldn't be flexible enough. It would basically tear itself apart. The system has to allow for movement of suspension and for the expansion of the fluid itself as it warms/cools. The engineers of these components aren't looking for perfect, they are looking for usable. Then there is also cost to be considered. You could possibly build a perfect braking system, but at what cost? Is the juice worth the squeeze?
Brake fluid can last for years in a sealed bottle. If you've ever taken the cap off to open a bottle, you'll notice there should be a foil seal over the opening. This seal and the bottle itself are not very permeable. They do not let much, if any, air through to the liquid inside. If the seal is broken, the manufacturers state it should be used within three months time or discarded. Brake fluid within a braking system should be replaced every two years. (Note: While this is a recommendation, you'd probably find most people never even think about the brake fluid in their vehicle and it never gets changed.) If the brake fluid is changed out as recommended, you'd find there'd be little to no worry about brake lines rusting out. Brake fluid, like engine oil, has a useful life span. It will do its job as required, but when it's past that period, should be changed so that negative consequences don't occur.
Brake fluid itself is very thirsty (hygroscopic). It wants to absorb water. (I use the term "want" loosely, because it really doesn't "want" anything, it just happens that way.) In physics, there's a property called the Conservation of Energy. Part of this law entails that energy, within a closed system, tries to equalize itself throughout the system. When one part of the braking system has more water in it than another, the system tries to equalize itself by trying to distribute the water equally. Think of it this way, if one brake fluid molecule has two portions of water and the molecule next to it has none, it gets jealous and takes one from its neighbor so they can then be equal. I realize this is example is a bit theatrical, but it's basically the way it happens. This is how the water gets down to even the furthest parts of the braking system.
