Well, your friend is only partly right, and that is because there several forms of blood clots that can occur.
In reality, any time there is bleeding, a blood clot will form. If you accidentally cut yourself, a blood clot forms in the cut that prevents further bleeding. If you fall and get a bruise that is visible, it is blood that has leaked into the tissue under the skin, which will form a diffuse clot. It is also possible to get bruising of deeper tissue, but if the blood is not near the skin, it would not be visible from the outside. If there is a larger amount of bleeding, causing a collection of blood that clots, it is referred to as a hematoma.
The type of blood clot that is worrisome is a blood clot that forms within a vein, referred to as a thrombus. This will usually occur in a vein that is inflamed (phlebitis), so the entire process is called thrombophlebitis. If a thrombus forms in a large vein, a portion of the clot can break off and travel to the lung, referred to as an embolus. It must be a larger vein to be a problem. Thrombophlebitis occurs more often in the legs, so is more studied in the legs, and a thrombus that forms in a deep vein below the knee or in any superficial vein is not of sufficient size to cause an embolus to the lungs. Therefore, thrombophlebitis is only worrisome when it involves a deep vein at or above the knee. Similarly, even if a blood clot forms in a vein in the hand or fingers, it would not be of a size that would be worrisome.
In your case, it sounds like a blood clot that would form in response to trauma, such as a bruise. Even if there is a thrombus in a vein in the finger, this would not be a dangerous thrombus, so there is no danger associated with such a thrombus.
In regards ***** ***** if it is "normal" for a vein to "pop," the answer is no, although it is common for a vein to result in easy bruising in person that are more sensitive. While not considered "normal," it also is not considered worrisome, particularly if the episodes are mild and infrequent.