This issue only needs to be tested in 1 device. In this issue you will download sections and courses and you'll have to inspect the network requests, so I suggest you to download small courses. Login in a 3.2+ site (it can be a master site) and open a course. Enable downloads in the course. Open the inspector and clear all network requests. Click to download a section. If a confirm is shown, clear network requests and confirm the download. Once the download finishes, check that the section icon changes to the right icon. In network requests, check that there's no request to  core_course_check_updates after the download (there could be some BEFORE the download, and they should always have the same list of modules). Now select "All sections" using the section selector. Open the inspector and clear all network requests. Click to download the section "All sections". If a confirm is shown, clear network requests and confirm the download. Once the download finishes, check that all the sections icons change to the right icon. In network requests, check that there's no request to  core_course_check_updates  during or after the download (there could be some at the start of the download, and they should always have the same list of modules). Now go to App Settings > Space usage and clear all the data from the current site. Go to dashboard. Open the inspector and clear all network requests. Click to download a course. If a confirm is shown, clear network requests and confirm the download. Once the download finishes, check that there's no request to  core_course_check_updates  during or after the download (there could be some at the start of the download, and they should always have the same list of modules).