What kind of companies could implement blockchain for transactions?

Hi,
I read an article on this site that mentioned that blockchain would be easier to implement for companies that are NOT working with large amounts of data. What kind of companies would that include, and which kinds would it not include?
Also, would it be more difficult for a company like a Wal-Mart that is consumer facing to implement blockchain than for a company like Mondelez (maker of Oreos) that serves as more of a supplier? My understanding of blockchain is that both parties in a transaction must be part of the network, and if it was a private permissioned network, you wouldn’t be able to have the consumers as part of it, whereas you would be able to have the other companies with which a company like Mondelez would be making transactions.
Thanks!

Joe