Did Bucky came back because of Jason?

I suppose that's technically a spoiler in this subreddit in the same way saying everyone but Odysseus dies in the Odyssey is a spoiler in a Greek mythology subreddit but I just want to cover my bases 🤷‍♀️ So I've been in a bit of a Red Hood kick lately and been reading things he's been in through out the years which got me thinking, I know he came back in UTRH which started in Feb 2005 (technically he made his first appearance in 2003 but I think that was a bit of a recon? Like they didn't intend for him to be the real Jason and was definitely just Clayface until Jason came back?) and I had to look it up but I knew Bucky came back around the same time (May 2005 according to google). So did Marvel just saw Jason came back and was like write that down ✍️ ✍️ ✍️ ? Or was it just a big coincidence? So bit of context about where I'm coming from but I was born in 2000 so I definitely wasn't reading any comics at 5 years old lol so I have no idea what the landscape was at that time or what storylines were happening I just know about that saying about how everyone could come back except Jason, Bucky and uncle Ben and thought it was strange for 2 of them to be resurrected within months of each other haha