There isn’t a “standard” T platform. The Red, like all the others, was built in chunks; the line from downtown Boston out to Cambridge terminated at Harvard until the mid-1980s, when they built a newer, larger station under Harvard Square and added the northern branch going out through Porter, Davis, and Alewife. (The natives consider things beyond Alewife to be outside the immediate solar system, and speak of them only in hushed, secretive tones.) Harvard and Porter have split platforms, with the lower level outbound and the upper level inbound. The rest of the new stations have island platforms, where the tracks bracket the waiting area. Central and Kendall are split platforms on either side of the tracks, where inbound is accessed from one side of the street and outbound from the other; they’re obnoxiously narrow and if you wind up on the wrong side, the only way to get to the right one is to go all the way back up to street level, try not to get pasted by one of the infamous Cambridge drivers, and go all the way back down through fare control on the other side.
As Ferret Herder says, it’s customary here to plow right up to the doors of the stopped train and plant yourself until they open. Bostonians, shockingly, do actually wait until people have disembarked before boarding. It only took me a couple of months here to spot the tourists, especially the New Yorkers and the Europeans, because they tend to make like the train will leave without them if they don’t jet through the doors the instant they open. The doors are semi-automatic, I think; there’s a safety mechanism of some kind that prevents them from opening until the entire train has come alongside the platform, but they’re under control of the driver. Usually there’s a T employee at the non-driving end of the train with a flashlight signalling the control cab that everyone’s aboard. There’s also a large angled mirror at the forward end of most platforms, so that the driver can see back along the length of the train. The drivers are surprisingly nice about this – they can and will re-open the doors for you if you sprint at them from the fare gate in a suitably desperate fashion.
It’s unusual, but it is mechanically possible for the driver to open the doors on both sides of the train; the only station I’m aware of where they do this is Park Street Under, which as it happens is on the Red Line. They open the outboard doors first, then a few seconds later trigger the doors for the island in the middle.
As for why she did it, I can personally attest that an awful lot of people on the T are operating strictly on hive-mind autopilot. I’m pretty sure you could walk naked through Park Street and maybe the buskers would notice. It’s not like NYC, where there are a number of different transit grids all sort of interlocked; Boston subways operate on a sort of hub-and-spoke model, and for the most part you just plant it on the train until you get where you’re going or hit downtown and change for a different color. A southbound train from Kendall is heading across the Charles and into downtown Boston.
I missed chizzuk’s comment before – having moved here from Arizona, I have to say that the people in Massachusetts take the whole “commonwealth” thing very seriously. I’ve had random strangers and T employees ask me if I was okay while I was crawling onto the Red to get my sorry germ-ridden tuchus home from work before I fell over. Someone pitched off the subway platform, people would charge over to help.