I'm afraid your de-icing provider was correct - quotes from my airline winter ops guide material:
In conjunction with the contamination check, prior to engine start, the engines must be inspected. Only hoar frost is permitted on the exterior of the engine. However, engine inlets, inlet lips, fans (check for rotation), spinners, fan exhaust ducts, must be checked free of frost, ice, snow and slush.
Engine anti-ice should be ON whenever ground-icing conditions exist or anticipated. High bypass ratio engines are particularly vulnerable to the formation of ice on and in the engine during low power ground operations. With engine anti-ice selected to ON, the leading edge of the inlet lip and inlet sensor systems are anti-iced, but the spinner, fan blades, and low-pressure compressor inlet stator are not.
Engine ice build-up can occur during taxi and ground holding even without visible moisture present. Industry events involving severe engine damage point to increased risk when the OAT is in the range from +5°C to -5°C and visibility is reduced in drizzle, rain, freezing drizzle or freezing rain.
When operating in this range,
Flightcrew should take the following precautions:
Engine nacelle inlet and fan blades should be carefully inspected as close to departure time as practicable to ensure that the face and backs of the fan blades are free of ice, as well as of snow or frost, that the fan is clear and free to rotate and no pooling of moisture is present. This is to avoid any engine damage, e.g. due to the ingestion of ice or to the accretion of snow that might block the fan. Manufacturers provide a ground run-up ice-shedding procedure to avoid engine damage. All such procedures presume that the engine was free of contamination when it was started. The engine warm-up time of at least 2 minutes (in order to avoid thermal shock) must additionally be respected, with the thermal shock risk being higher in icing. Refer to the QRH for static run-up procedures.