Yes we profess that - it’s in the creeds.
It’s generally not an exclusive claim - we generally view the OHCAC as where the Gospel is proclaimed and the Sacraments are administered.
From an outsider’s viewpoint, it may look like a silly claim - our church has issues, our liturgy is a mess, and our numbers as small. Yet those things have nothing to do with our strength and refuge in Christ and Him crucified.
As I understand it, the larger sticking point among Catholics to our claim is Apostolic Succession - in that while we desire it as a continuation of the Western Church, we’re content with holding to the apostolic teaching of the historic church.
I certain there will be wiser Lutherans on this forum that will expand on this - I just wanted to get my $.02 in so it looks like I’m paying attention