I've created a simple Grid field with a file field inside:

related_items:
    type: grid
    max_rows: 3
    fields:
      title:
        display: 'Title'

      content:
        display: 'Description'
        required: true
        type: textarea

      image:
        display: Image
        required: true
        type: file
        allowed: [png, gif, jpg, jpeg]
        max_files: 1
        destination: assets/img/related/
        instructions:
          below: 'Images should be at least 340x195 pixels.'

The problem is that in the control panel, the file fields accept multiple files, despite the max_files value. If I'm reading the docs correctly, this seems like a bug.