Core doesn't want Rebble's data. They want the data from the original Pebble store, which is not owned by Rebble. It's the work of thousands of independent developers and it should be shared freely, not kept in a walled garden with "no scraping" terms added on. It's actually offensive that Rebble is using other developers' data (that they originally scraped from Pebble) as a bargaining chip in their contract negotiation that they made into a public squabble.
I don't think that's quite right - Rebble has updated a number of these apps to keep them supported. As sibling commenter posted, the original apps are available publicly.
I think that’s the crux of the issue is rebble isn’t under any obligation distribute them open source, unless say the original app had a “copyleft” policy?
AFAIK the original apps were individually licensed by the creators... so Rebble would need to have permission before claiming anything for their own except in the case of explicit permissive licenses (like MIT). In some cases (copyleft licenses) Rebble would be required to make their maintenance also open source.