Grayscale is a single channel mode containing brightness only information based around a single hue – normally gray – which provides a true monochrome image. In this mode a data level of 0 would be black and 256 would be pure white – in print terms this will be paper white. If you convert a colour image to this mode the data in the file will be truly neutral and should give rise to a colour neutral print. If the print shows signs of a colour cast (other than any base tone of the paper itself) this would indicate that the colour management setup or, more likely the printer calibration, is incorrect.
Note that a monochrome image can be, and often is, an RGB mode file with three channels in which case neutrality would be evidenced by the pixel values in all three channels being identical – e.g. R128 G128 B128 would represent a mid gray.
The Info Pallette in Photoshop lets you inspect the values of individual pixels in the image so this provides a useful tool to verify that areas of the image you wish to be colour neutral are indeed so. Again, if such areas print with a colour shift then there is something adrift with colour management or printer settings/calibration/profiling. If the numbers show that the file data is colour neutral but the area appears to have a colour shift on screen this would indicate a badly calibrated monitor. 
One other significant element in colour perception is ones own eyesight and different people see things “differently” – have you had your eyesight tested recently ? Have you ever had a colour vision test?