The influence of transparency changes what you see on screen.
Check with the Separations preview, Window > Output > Separations, if the color values change. If not, it is only the known screen issue, if so, you have indeed a transparency included in the Illustrator file, which will make changes.
From Illustrator to InDesign you should only use AI files or PDF/X-4. Never use EPS or PNG, both are decreasing your quality in InDesign, as EPS does not support colormanagement or transparency, and PNG does not support vectors, nor CMYK nor any other transparency than alpha-transparency.
Does the transparency blend space (Edit > Transparency Blend Space...) match the color space of your art and background? Washing out is frequently associated with CMYK blending of RGB art.
Thanks everyone for your help. I figured it out. I had made the background texture in photoshop and converted it to gray scale. Turns out I should have converted it to CMYK. Once I did that everything evened out in my indesign document.
Kind of a Do'h moment but oh well.
Thanks again fro everyone's quick responses.
Turns out I should have converted it to CMYK.
Just be aware that the conversion to CMYK makes a 4-color black and that's the reason its appearance is a darker valued black. Your document's CMYK profile is showing the difference between black only 0|0|0|100 and a 4-color black conversion like 75|68|67|90, which is what will happen on an offset press
So if he is trying to limit the project to 3-4 colors should he convert it back to grayscale?
If by 3-4 colors you mean spot colors and printing with custom inks then yes, but something tells me that is not the case.
The CC print apps use the document's CMYK profile to accurately display how CMYK black mixes will print on press. In some cases you have to turn on Overprint Preview to see the effect. When there is transparency on the page the preview depends on the document's Transparency Blend Space. If it's CMYK, blacks get the accurate preview whether Overprint is on or off.
When you print on uncoated papers and assign an uncoated CMYK profile the effect is more noticeable. Here a rich black 65|50|50|100, 100% cyan + black, and 100% magenta + black over black only:
Uncoated GRAcol assigned:
US Coated Sheetfed: