Firstly, that the Milanese think so little of Celtic's prospects that they were utterly indifferent to anything the Scottish champions might have to say on their arrival. Or secondly, that those who follow the seven-time European champions have been through far too many campaigns to rush to an airport when any opponent - Scottish or otherwise - flies in for a group game in the middle of September.
This is Milan's 17th campaign in the Champions League and their 11th in the last 12 seasons. They are part of the tournament's furniture. Injuries and a sense that the current team is an unproven shadow of the great Milan teams has caused a justifiable mood of optimism about Celtic's chances this evening, but a sense of perspective is always a valuable companion at this level. In Alessandro Matri and Mario Balotelli they have heavyweight artillery to turn on the visitors.
Celtic took 10 points in their successful group campaign last season and that more than entitles them to the upbeat mood in which they travelled yesterday. But when their bus is given its police escort through the streets of Milan tonight, San Siro will loom large, larger and more imposing than it seemed when they trained between its empty stands last night. It is one of only six football stadiums in Europe that can hold more than 80,000 fans. When the Rossoneri disposed of PSV Eindhoven in the play-off round, the attendance was 50,000. A bigger crowd is expected tonight.
If Milan are battle-hardened Champions League veterans, then Celtic, too, have added some valuable layers of experience over the past 12 months. There comes a point when a club from one of the smaller countries handles a fixture like this without coming across like rubbernecking tourists, gawping players out on the pitch taking photographs of the surroundings on their smartphones. Celtic are at that point. "We're past all that but at the end of the day they are footballers," said Neil Lennon. "All these clubs have great history and tradition so it's natural that you want to take some memories from it. They might not get the opportunity again.
"But we're here to do what we did last year. We want to compete in every game and see where that takes us. I want to savour all the games. Last year was my first time [as a manager]. This is my second year and when I look back I sort of think: 'I wish I had done more of that'. This time I want to take it in and enjoy it.
"San Siro is a brilliant stadium and a great venue. We're playing one of the sort of aristocracy of the Champions League so it's a game to savour and one to look forward to. But our team is full of players who have played for their countries for quite a while now so they've been up against this type of opposition before. The campaign last year showed me that they can handle it. For being a youngish side there's plenty of experience in it as well."
No single fixture is more reassuring for Celtic ahead of tonight than the 90 minutes at Camp Nou last October. Against Xavi, Andres Iniesta, Lionel Messi et al Celtic had only 18% possession to Barcelona's 82%. The corner count was 15-1. The attempts on goal 20-4. But Celtic took an early lead through Georgios Samaras and defended excellently even after conceding an equaliser. Only in stoppage time did Jordi Alba find a way through again for Barcelona. Lennon has seven players from that game who are likely to start again tonight: Fraser Forster, Emilio Izaguire, Efe Ambrose, Charlie Mulgrew, Mikael Lustig, Scott Brown and Samaras. If they could handle Camp Nou and that sublime Barcelona team, and emerge with dignity after a hugely competitive game, they can they need not feel overawed in Milan.
"I think it will be difficult to emulate what we did last year," Lennon continued. "I've said that all along. But you never know. You can't dictate what neutrals or other people think about your chances. You just have to concentrate on what you're going to do. Taking on AC Milan in Milan is as difficult as it comes. We respect that but we're playing well so there's no reason why we can't go into the game with some confidence.
"I like Balotelli, his individuality. He's a world-class striker already. The majority of Milan's good play comes though him. He's a pivotal player at the front of their attack. People look at him and say he's a little bit moody and all that but I think the more you rattle him, the more he responds to it. But listen, we can't just concentrate on Balotelli. There are so many good players that we need to be wary of as well. But I like him, just watching him play. Put it this way: I'd have in my team."
Lennon has plenty of options. His back four would seem fairly settled, with Brown and Mulgrew protecting them at the base of midfield. Milan look comparatively vulnerable to pace on the counter-attack, which could mean Derk Boerrigter being preferred on the right and Samaras left, with Kris Commons in the hole. Adam Matthews is another option. Up front Anthony Stokes' form has been excellent and it would be harsh if he was a substitute. On the other hand, Teemu Pukki was signed for nights like this.