I believe it to be correct, at least in the improvised music idiom. Lacy's solo LPs/recitals were directly inspired by Braxton, as I understand it. Parker, McPhee, Mitchell, Abe, Hemphill, Lake, Brown... all of those came later.
The Hawkins soli were released on shellac 10"s and I'd call those EPs at most, not albums. The Hawkins on Asch is essential material, IMO.