Can a foreign object pressing against a vein cause a deep vein thrombosis?

Yes: Compression of a vein for long periods of time with decrease in venous blood flow can lead to thrombosis. Example, compression of the deep veins of the upper arm as they pass over the ribs into the chest can lead to thrombosis. Patients with an extra cervical rib have a narrow passage for the veins to enter the chest. Overhead work, like hanging wall paper can compress the vein against the rib.

Compression thrombos: Pressure resulting in obstruction of a large vein can cause thrombosis and phlebitis. Directly or indirectly through clot propagation, a deep vein may become involved. Reduction of normal blood flow(venous stasis) predisposes to thrombosis. Other factors (inheirited, birth control pills, smoking, malignancy, bedridden) encourage this process.