The healthcare industry does pour a lot of bribe money into preventing reform; see e.g. killing anti surprise billing legislation. However, the bulk of research into why the US doesn't have universal healthcare access points the blame at the blocking minority of Americans who'd prefer not have healthcare for themselves if the alternative is people lower on the social hierarchy (read: non-whites) having healthcare.
This is likely a far harder problem to fix than the already nearly insurmountable problem of excessive corporate influence over government policy.