I don't know, I've always sat on the fence on this one.
Johnson claimed that he threw the fight in order to receive a pardon and cash to allow him back into the USA to see his ill Mother. The reason he claimed that he left it 26 rounds was because the envelope didn't show up till round 25. After his wife received the envelope (which Johnson claimed turned out to be empty) he threw the fight in the next round.
Johnson swore to the above on the the grave of his Mother years later. A pretty classless thing to do if it wasn't true!
A few other thoughts:
1) In the mid rounds Johnson hit Willard with some superb combinations, driving him across the ring. If he had agreed to throw the fight, he was in danger of knocking Willard out!
2) The punch that Willard hit Johnson with to knock him out did look pretty useful!
3) Johnson was clearly not 'out' as he held his hand to shield his eyes as he was counted out.
4) Would Johnson's wife be so stupid to accept an empty envelope? Or not to check it's contents?
5) Johnson was 37 at the time (which was considered ancient for a world class boxer back then) and a little podgy. A fight set for 45 rounds in the Cuban heat could exhaust anyone......and Johnson was pretty active in some of those rounds.
I honestly don't know! But I think long term losing the title to Willard was probably best for Johnson. Dempsey was only a few years away, and I wouldn't have wanted to be a near 40 year old facing prime Dempsey.......