The former Spain captain and his compatriot brought a different dimension to Sam Allardyce's side, offering a combination of defensive pedigree, technical ability and vision that Brown believed was almost impossible to find among English centre-halves at the time.
It was a distinction he once put directly to Sir Bobby Robson. The legendary former England manager, who had also worked extensively in Spain and understood the country's football culture, needed two and a half hours to come up with an answer.
The story began with a problem. Campo, who had arrived at Bolton from Real Madrid in 2002, was an extraordinarily adventurous defender. His instinct was to play forward, take risks and find passes that other players had not even considered. It was an ability that could be thrilling, but it was not necessarily what Allardyce wanted from someone operating at the back.
Brown, who worked alongside Allardyce as part of the Bolton coaching staff, remembers the first game Campo played at centre-half.
"Sam used to be up in the stand, I used to be down on the touchline," Brown told Football Presse. "First half, I'm witnessing a couple of things and Sam's obviously witnessed a couple of things, and he's seen it from a tactical perspective. I'm seeing it from what, you know, body language and what I'm hearing from the touchline."
A message came through the coaching team's communication system.
"Sam just said, remind me Brownie, I'm not going to have a go at him at half-time, or anything else, just remind me Brownie never to play Campo centre-half."
Brown initially wondered whether Bolton were going to send the Spanish defender back to his former club, Real Mallorca, but Allardyce had another solution.
"No, no, no, no, no. See that midfield berth? That's his."
Campo's adventurousness had become a problem because he was attempting things in dangerous areas without always having teammates available to receive the ball. Brown likened it to the modern tendency to play intricate passes around the penalty area, except Campo was sometimes attempting it without the necessary support.
"Campo was all for that. Ooh, but today you've got four or five players you can play five-a-side with. Campo had nobody. He was looking for a pass and everyone was like, whoa, you're on your own, son.
"But Campo would still look to play and he then realised, I've got nobody to play with. So we had to get him away from the goal."
Moving him into midfield allowed Bolton to use his passing ability while removing some of the risks associated with playing him in the defensive line. The arrival of Hierro added another remarkable dimension.
Fernando Hierro and the extraordinary vision of Campo
Hierro had spent 14 years at Real Madrid, winning three European Cups and six Spanish league titles, and had established himself as one of Spain's outstanding defenders. He had also earned 89 international caps. By the time he joined Bolton in 2004, he was 36, but his understanding of the game remained exceptional.
Brown was particularly struck by the relationship between the two Spaniards.
"And the respect that Campo had for Hierro was phenomenal. So when we played Hierro behind him, I think it was Bruno N'Gotty, Fernando Hierro, and we had Ivan Campo in front."
Campo's contribution was not simply about protecting the defence. His ability to recognise passing opportunities before anybody else made him an unusual presence in midfield.
"He had the biggest mop of hair, as you know, and how he could see a pass outside of that mop of hair, I just couldn't believe it.
"When he saw a pass, you look at him and go, when did he see that? When did he see that pass? You're trying to work it out, and he had looked minutes before anybody else. He had a picture minutes before."
For Brown, that was a significant part of what made Campo such a special footballer. His experience at Real Madrid had given him an understanding of space and possession that was difficult to replicate. Hierro brought a similar pedigree, and together they gave Bolton two defenders who could influence a match in ways that went beyond their conventional positions.
It was at an end-of-season League Managers Association dinner that Brown decided to test that belief against one of the most respected football minds in the country.
Sir Bobby Robson had managed England, taken Ipswich Town to major domestic and European honours and worked at some of the biggest clubs in Europe, including Barcelona and Newcastle United. Brown knew him well enough to approach him for a conversation.
"I went up to Bobby, who I knew quite well. I just said, Sir Bobby, obviously. Bobby, I said, you know, we've got Fernando Hierro and Ivan Campo at Bolton."
Robson acknowledged that they were great players. Brown then put him on the spot.
"You name a centre-half in England. You name a centre-half that plays in the Premier League in England or for England that can play in midfield. We've got two Spanish centre-halves that can play midfield and not just playing, they grace it. You know the Premier League. You name one."
Robson did not immediately produce an answer. Brown continued with the evening, but the question had clearly stayed with the former England manager.
"He didn't come back to me until after the dinner. So it was about two and a half hours later, and the only one he came up with was Gareth Southgate."
Southgate, then an established England international defender and Middlesbrough captain, was the name Robson eventually offered.
"He said he was the only one he could possibly think of could, at the time, play centre-half but also playing the one in front."
Brown acknowledges that Bolton also had outstanding midfielders capable of operating alongside a deeper player, including Jay-Jay Okocha, Gary Speed and Kevin Nolan. The point was that Campo and Hierro did not need to be pushed further forward to influence games. They wanted to receive the ball with the play in front of them.
"That baffles me as well, I must admit. But Sam, he played them both there just to get them away from danger."
It was an unusual solution to an unusual problem, but one that captured the thinking behind Allardyce's Bolton. Hierro and Campo were not simply defenders who could pass a football. They possessed the awareness, composure and technical ability to give the team something different.
And when Brown challenged Sir Bobby Robson to find an English equivalent, the eventual answer said everything about the quality Bolton had brought together.