It does look bad in the sample they attached. The round letters extend way above their overshoot points, which makes them look larger than the glyphs with the square terminals that stop at the x-height.
You didn’t happen to outline the fonts (or even worse, rasterize them) on whatever it was you sent them, did you. If so, this removes the hinting from the font that is added to mitigate these sorts of pixel rounding errors when viewed on lower-resolution displays.
If that’s not the case, rounding errors are still my best guess, but it’s likely due to some glitch unrelated to the font. Whatever the reason, though, if you have a legitimate copy of Helvetica Neue, the outlines should be fine, and the problem will go away when viewed or printed from a higher-resolution device.