Download all records for an activity

That probably means that you don't have permission to download the individual records. From what I remember, you can download records if a) they are ones you have input, b) they are a group that you are set up as a verifier for, or c) they are for an activity that you have set up and were added via a form setup for the activity. That means if the activity captures records not added via a specific form, e.g. it is an activity to collate all species within an area regardless of who input them or what form used, then you can only donwload a species list, not the records themselves. 

The best bet probably to email iRecord support who might be able to supply you with the data.