Breaking 126.96.36.199 into separate paragraphs:
For Lion through Bear ranks, if the activity is completed outside of the den meeting, the parent, adult partner, or another trusted adult may sign in the Cub Scout’s handbook, indicating the Cub Scout has done their best to complete the requirement. The den leader then records that requirement after consultation with the family or the Cub Scout to confirm completion.
If the requirement is completed in a den meeting, the den leader signs the handbook and records the requirement. Den leaders may delegate an assistant or parent who helps at meetings to assist with the approvals.
For Webelos and Arrow of Light adventures and ranks, the den leader signs for approval of all requirements, unless the den leader delegates this responsibility.
For Lion-Bear, if a requirement is done outside of den meetings, then normally the only requirement is that the Den Leader consults with the family to confirm completion. I don’t see anything that requires the parent / family to provide proof.