Many printers do use color inks to print in greyscale. Check your owners manual, it may say something about it. For example
The Canon Pixma IP5300’s manual states; “Printing in grayscale may use colour inks”.
And from HP’s website: “For black and white images and photos, a blend of colors called “composite black” may be used to achieve significantly better image quality and smoother gray tones than can be accomplished with black inks alone.”
I assume most all printer companies are this way. According to HP’s website, the quality is much better when colors are added to the black ink and also improves the printer reliability. HP mentioned that most of the printers give the user the option of turning off “composite black” and using only the black ink without the colors.