Ayton's team is trying to control the narrative just like the Suns are. Their job is to make Ayton happy and represent him while the Suns need to deal with all players. It's apparent the Suns struck 7 other deals this summer (Paul, Payne, Shamet, Bridges, McGee, Nader, Frank, and Payton). Not a peep from those sides about misrepresenting intentions, being deceptive, or not willing to negotiate. Ayton's camp is the only one that had difficulties and didn't get what they were after.
Choose who you want to believe. That's everyone's own decision, but I'm leaning towards believing the side that managed to please literally everyone else. It's not like James Jones and Sarver aren't disappointed that Ayton wasn't extended. They wanted it to happen also and it didn't work out.
Two sides of the story have come out. James Jones version of events doesn't contradict Ayton's side in the same manner Ayton's side does the Suns. The Suns could have countered the 5 year max demand with 3 or 4 years and been told it's 5 or nothing. Meanwhile Ayton's side said they wanted 5 and were only accepting 5 years max so why do they care if a 3-4 year offer was made? Both sides admit Ayton wanted 5 years max or nothing also.
I'm not sure what is gained by lying about lesser deals other than controlling the narrative. It'll be obvious the Suns don't want him for a 4 year max if they don't match next offseason so it'll catch up to them if they're lying. There's no way to say Ayton's side is lying though outside there of Ayton firing them, which is unlikely unless he would have taken the 4 year deal. So we won't get answers beyond what is available now.