I did a bio undergrad and one of my professors was involved. She was adamant that the Human Genome Project finished ahead of Celera and that the HGP published reference data that Venter and team fundamentally relied upon to even have their shotgun approach work.
here are technical details, both were more or less independent, the celera sequence did include data from the other side as useful reference points but the assembly would have happened without it. https://pmc.ncbi.nlm.nih.gov/articles/PMC123615/