In one sense I think you are right. It is hidden in the Genesis 12:2-3 statement. But in another sense, this statement by God in Exodus 15:26 was NOT announced till after the Israelites were loosed from Egypt's clutches and power, after their baptism unto Moses (1 Corinthians 10:1-4) Certainly uttered BEFORE the Mt Sinai covenant, but included in the blessings announced in Leviticus 26 and Deuternomny 28 - because when you examine the curses coming to them if they turned away from the Lord and disobeyed then terrible sicknesses would come upon them along with other calamities. So Healing was in the Mosaic covenant, and just before it. Solomon also asked God to heal those who prayed towards the Temple.
Also consider that whether we are discussing the convent with Abraham, or with the people of Israel as mediated through Moses, these are still inferior covenants to the new covenant in Jesus Christ, which is brother Osborne’s main point: if the Lord healed the people so completely under an older covenant, then how much more certainly will He do it under the New Covenant in His own blood, based on better promises.