If the neighbor(s) will not execute an agreement allowing access, a lawsuit would be necessary. And it's definitely NOT a given that the court would award the relief sought. All of the elements of an easement by necessity (or prescriptive easement, depending upon the facts) would need to be satisfied... read SD case law to find out what would need to be proven. At some point that land was subdivided -- how, when and by who is crucial. Also the nature of the current "access" -- whether it has been hostile or permissive.
The good news is the title insurance carrier has allowed the claim and will likely pursue an agreement with the necessary property owners OR fight the legal battle if necessary. And it could cost many, many thousands of dollars in legal to eventually win or lose. The fact that title insurance includes defense expense is a great lesson in why chosing NOT to purchase owners coverage is stupid.
Of course if the court doesn't award the easement, the title insurer would likely pay out on the title claim based upon the lack of access. I would say that's not a total failure of title so not a full policy payout. It would be a good time for @Peter Walther to chime in on this. He'll probably correct some of my analysis as well!