It's not quite clear from the court record, but I think that what was happening in the court case was that Gray had entered into a structured settlement with Allstate, and that Peachtree was seeking to purchase certain rights with regard to the structured settlement. In many states, such transfers require court approval.
But, a little digging around shows that the Allstate settlement had NOTHING to do with any vehicle accident or spinal injury. A quick search of the Maryland court records shows that Freddie Gray's twin sister, Fredericka Gray (creative naming, right?) also had a structured settlement with Allstate that Peachtree was trying to purchase:
Some further digging reveals news articles that refer to a lawsuit brought by Freddie and Fredericka Gray against the owner of a building where they lived growing up, alleging that they were harmed by lead paint in the building. (Source.) According to the article, the Grays entered into a settlement with the former landlord, whose name is Stanley Rochkind.
Finally, some further digging reveals that Allstate Insurance Company has sued Rochkind. Turns out that Rochkind has an umbrella insurance policy with Allstate, and that Allstate has sued Rochkind in order to determine whether the insurance policy required Allstate to pay a claim to related to a different lead paint lawsuit brought against Rochkind:
Taken together, it is pretty clear that the Allstate structured settlement was related to the lead paint lawsuit, not to any previous spinal injury.
In other words, the story at link is complete and utter horseshiat.