Color negative film is designed with an orange mask/base, so an uncorrected scan or photo of the negative will indeed show a strong cast. The reason scans still work is that the mask is corrected during printing or scanning.

Traditional optical printing handled this with color filtration/exposure adjustments. Dedicated film scanners do something similar, using scanner software and channel/exposure balancing to neutralize the orange mask before or during conversion. Many scanning programs also let you choose “color negative” or even a specific film stock because different films have slightly different masks.

With a digital camera copy setup, you capture the orange-masked negative first, then invert and correct it in software. That’s why camera-scanning color negatives usually depends heavily on post-processing or negative-conversion software.

This is much easier for slides and black-and-white negatives, because they don’t have the same orange mask. So your reasoning isn’t wrong—the cast is really there. The missing step is that scanners, darkroom workflows, or software compensate for it.