Why does Asset Export in Adobe Illustrator CC 2017 add extra pixels to pictures?

Question

Design

I am designing a website. I throw icons 32x32, pictures (clipping mask) 600x360, logo, other graphics into the Asset Export panel.
As a result, the icons turned out to be 33x33, the photos 600x400 (and it's not that the image inside the mask has such a height, no, the images have a variety of sizes inside the masks) and other annoying deviations. Part of the graphics exported normally. All in 1x scale.
What is wrong and how to fix it?

Answer 1

Finding a solution to this problem took me 15-25 seconds along with reading. The question is in integer coordinates of the artboard placement. Drive them in with pens or use the artboard positioning tools in Ai.
This works when creating multiple artboards of the right size.
When working through Exports for Screens (creating a list of set permissions for export), it also continues to be weird.