CVSTs happen in women taking oral contraceptives at a rate of 1 in 1000 per year?
Estrogen is a clotting factor and if you have elevated risk markers (like Factor V Leiden) that risk skyrockets when you add extra estrogen.
Many insurance companies get angry when you ask for blood tests to check before getting birth control (my wife was charged an extra 1k because she requested a blood screening after she learned she had a history with clotting).
I've had a cousin hospitalized for birth control related thrombosis, so again: my input could be biased here.
Does 1 in 1000 women taking oral contraceptives having rare strokes every year sound right to you?