In a Coolidge X-ray tube, increasing the current passing through the filament increases the intensity of the emitted X-rays without altering their penetrating power (hardness).
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The statement is true. Filament current controls the rate of thermionic emission (X-ray intensity), whereas accelerating voltage controls the energy and penetrating power (X-ray hardness).
The statement is correct because filament current solely regulates the rate of thermionic emission, controlling the total number of electrons striking the target per second and thus the intensity of the X-ray beam. Penetrating power (hardness) depends on the accelerating potential difference, which dictates maximum electron kinetic energy and minimum X-ray wavelength.
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Independence of X-ray Intensity and X-ray Hardness (Penetrating Power)