The mechanism for this is well documented. However, most references say that icing in the intake duct cannot, or does not, occur with fuel injection sysytems
What sources say that induction ice doesn't occur? I've never seen one. Perhaps you're confused about what you're reading.
There is nothing about fuel injection that affects induction icing. In other words, in a discussion on induction ice, fuel injection is irrelevant; it has nothing to do with the price of tea in China.
Several kinds of induction ice can occur. Carburetor ice you've already mentioned. In aircraft equipped with carburetors, ice at the throttle plate and venturi area within the carburetor can experience icing which occludes airflow, or which impedes the fuel jet, starving the engine of fuel and airflow. Two types of carburetor icing occur; one involving use of the idle jet, usually with a closed or nearly closed throttle plate, and the second involving operations at high power settings or anything above idle, in which the main fuel jet is partially occluded or the entire venturi throat and becomes blocked. In practice, it takes fairly little ice to cause engine problems in the carburetor, and very little change in carburetor air temperature and mass airflow (throttle position and engine RPM) to affect a change in the rate of ice buildup or loss.
Two other types of induction ice occur, plus the hazard of ice passing through the induction and into the engine to cause blockages or damage.
Piston engines utilize an alternate air door for the engine inlieu of carburetor heat, as there's no carburetor to heat, and the mechanism of icing is different (or more appropriately, the manner in which icing affects the engine is different). Some engines use manual alternate air doors in the event induction air is blocked. Others use automatic doors, and some engine installations utilize "suck doors" that are typically held closed magnetically and drawn open if the induction is suddenly blocked. These latter doors have been responsible for a few engine failure when the door itself failed and was drawn into the induction, blocking airflow, and causing an engine failure. In fact, a fatality occurred at a corporate department where I worked due to this very thing.
Induction ice can form at the air inlet, in an injected piston engine installation. This often forms across an air filter. In most installations, there's no remedy for this, other than the use of alternate air.
Induction ice can rarely form inside the induction area, though most engine installations prevent this by using inlet filtering at some point in the induction (either actually at the inlet, or sometimes farther inside the airplane). Icing can form on the throttle plate, or in some cases can build at a bend or turn in the induction housing or tubing. This generally only occurs when a significant enough change in the induction diameter causes a change in airflow velocity and consequently pressure, and only when sufficient moisture is present, and even then only when ideal freezing conditions exist. This is unusual. Ice can form in the induction itself (rarely), or on the throttle plate.
Some installations use changes in the direction of the airflow to remove contaminants. This is more common in turbopropeller installations, especially PT6 installations, where the air induction is toward the back of the engine, rather than the front. Where a change in airflow direction occurs, it's known as a "mass particle separator," which allows ice, debris, birds, etc, or anything with mass to avoid being drawn into the engine directly. Various means such as "ice vanes" are used to increase this action in the presence of precipitation or contaminants (the King Air and Piaggio, for example). Most piston installations don't get that fancy.
I've never seen a reference that suggests induction ice doesn't occur in injected engines. In fact, I've never seen a reference that doesn't warn that induction ice can occur in injected engines, and that makes a provision for an alternate air source to accommodate that potential event.