First, let's put the fantasists to one side. There's no anti-American bias at Cobham. And there's no belief amongst the coaching staff, including manager Frank Lampard, that Pulisic is the wrong fit for his system. Such claims, as we've seen in recent days, is simply the stuff of mischief-making.
Indeed, the opposite is true. Lampard and his backroom team know they have a potential world-beater on their hands. They know the ability Pulisic possesses. But they need the American to come out of his shell more. To stretch himself amongst his teammates and on the training the pitch. "He needs to fight for it", as one Cobham source told this column a week ago.
As mentioned, no-one doubts Pulisic's ability inside Chelsea. Like us on the outside, they've already seen it in glimpses in preseason and the limited action Lampard has handed him thus far. And we say handed, as for the moment the consensus amongst those pushing the witches hats around is that Pulisic isn't doing enough in training to warrant selection. And it's not so much what he does in drills and bounce games - "he keeps it all nice and tidy" - but in his overall drive to get himself ahead of teammates currently occupying what should be his place. As Jurgen Klinsmann, the former USA coach, put it this week, Pulisic needs to get "nasty".
If Pulisic doesn't have Klinsmann's number, then you hope his father, Mark, can reach out to the German great and have him call his son. Klinsmann's interview this week discussing Pulisic's problems nailed it. He hit many of the points our source made last week. Not just the need for the 21 year-old to show a willingness to compete for his place, but also how he is in unchartered water. As we were told, this is the first time in Pulisic's career where set expectations are waiting to be met. The staff at Chelsea understand this. They've seen it before. But it's up to the player to cut loose from what he's known.
As Klinsmann says, "He's a very special player, he's tremendously talented, but this is a big step, because Borussia Dortmund was also basically the club where he got formed into a professional player.
"He came out of the youth system there, he moved himself up, he had all the support within the club and now going to London..."
We'd also add Pulisic's international career to Klinsmann's assessment. The German capped Pulisic at 17, with no great expectation. At that stage in his career, everything he achieved at senior level was a bonus. It was all about learning his craft, gaining experience. He was given the time and space to adjust to international football. To meet it's demands. Just as he was with Dortmund.
But now he's in a very different environment. A reputation needs to be built. New relationships established. And a realisation must dawn that he's not entitled to anything. No-one is going to give him a free pass. Or better yet, a free place in the manager's XI.
Klinsmann again: "He will go through a phase now where more and more he needs to bring his elbows out to fight himself through the system, at Chelsea it goes from game to game, week to week.
"You're basically in training, and you have to tell the coach: 'I'm in, I'm going to start this game, you have to become nasty to make yourself a starter."
From what we know, Klinsmann and Lampard aren't close. But the German was definitely helping Chelsea's manager this week. Klinsmann essentially parrotting what Lampard had stated after leaving Pulisic on the bench for the home defeat to Valencia.
"He's shown some really good moments," reasoned Lampard, "but what he has to do, as all the players have to, not just the wingers, is reach levels in training daily that make you sit up and go 'here's my team selection and that's actually affected it, I have seen good stuff'. That's the same for every player in the squad."
Training ground form and application is what makes Lampard tick. It's what transformed a chubby, but talented, midfielder at West Ham, into a modern day great at Chelsea. Going through the motions. Doing just enough to get by. It just won't survive within a Lampard-managed squad.
Pulisic has been given some great advice this week. And he can make it at Chelsea - so long as he acts upon what Klinsmann says.