On paper, it seemed about as good an idea as Peter Perfect climbing into the same wacky flying machine as Dastardly and Muttley.
But the visit was all in good nature; the Spaniard came bearing gifts for Lance and Johan - trinkets of appreciation for their roles in helping him win last year's Tour.
Honouring a race tradition started by Greg Lemond back in 1990, Contador handed over a couple of inscribed watches.
Rumour has it Armstrong's watch is currently running 50 seconds late with manufacturers fearing the piece could fall even further behind when worn at altitude.
Armstrong, of course, had no time to greet his former team-mate, preparing instead for the imminent visit of Prince Albert of Monaco. "I didn't speak to him," admitted the seven-time champ. "I was in the back of the bus. I didn't see him. I was in the middle of something else."
Maybe that explains his 10.34am tweet: "There's a foul smell in the bus all of a sudden."
Bruyneel did, on the other hand, manage to spend a moment chatting with his old Astana minion. "He comes out to the bus on his own initiative," he said. "I think that says there are no hard feelings. It's nice he thought about (the present) and brought it to the Tour."
Initially dismissive about the whole episode, Armstrong later told reporters that Contador's act was "very generous".
In the most flagrant twisting of the facts since Bill Clinton denied having sexual relations with that woman, Armstrong added: "Obviously he recognises he had the support of a great team and it's a nice gesture."
The Texan then returned to his laptop, logged onto Ebay and put a "first hand, never used, unwanted gift" Festina time-piece up for sale, starting price $25.
Return of the Manx: In other news today, Mark Cavendish finally got the monkey off his back (no, not Gorilla Greipel) with victory in stage five.
Twenty four hours after the Manxman was somewhat brutalised by his fellow sprinters in Reims, the Briton soared to an emotional victory in Montargis.
There were no nasty hand gestures as Cav crossed the line two bike lengths ahead of Gerald Ciolek, just sheer relief and unfettered emotion.
Mark "Tough Guy" Renshaw managed to outmuscle Thor Hushovd after the two came shoulder-to-shoulder, before leading Cav through a tight Garmin sandwich in what was the greatest launch since, erm, Danilo Hondo's the day before.
This time, Cav had the strength and determination to see off the job and make many media commentators - yours truly included (to an extent) - eat humble pie. You're only as good as your last race - just like pundits are only as good as their last blog - and the 24-year-old was in a league of his own under the highest temperatures so far in the race.
Green may be but a dream, but Cav's back and hungry for more. His floods of tears on the podium showed an entirely different Mark Cavendish than the one who swore, spat, trounced, upended and generally belittled his way through the past year or so.
The new Cav seems likeable, human, humble and inspirational. His press interview about now realising what it's like to crash down to earth from a cloud was honest and from the heart. If he's learnt the big lesson he claims he has, the past eight months of his life will quite possibly be more important to him in the long run than the previous eight months in which he was winning everything.
And for the viewers it's great: not in a long time have bunch sprints been so gripping.
Quote of the day #1: "They'll get a good suntan but apart from that..." Ex-pro and l'Equipe pundit Jean-Francois Bernard sums up the chances of stage five's breakaway.
Quote of the day #2: "The man with pure speed in his legs." If commentator Phil Liggett is right then David Millar better stay clear of the border.
Word of the day: Ci-oh-lek - n. the sudden realisation that someone you forgot existed exists. Eg: I turned on the TV and saw Hoby from Baywatch prance around on the beach - man, was I ci-oh-leked.
Stage six prediction: The longest stage of the Tour finishes in the small town of Gueugnon, renowned for its stainless steel industry. So, how about victory for Jens Voigt - hard as iron with his face showing no signs of those nasty scars picked up on last year's race.
If it comes to a sprint, it's worth bearing in mind that the town's football team, the lowly FC Gueugnon, were surprise winners of the French Cup in 2000 - inspiration for an old underdog like Robbie McEwen perhaps?
Plat du jour: A good one this - Charolais Boeuf Bourguignon with a bottle of Burgundy rouge. Not ideal if you have to spend the next day in the saddle, mind.
Peloton prattle: Which domestique actually likes fetching water bottles because it reminds him of the time he played the camel in his school nativity play?
Uses for Alessandro Petacchi #1: One of the Ramones - here today, gone tomorrow.
Follow Blazin' Saddles throughout the Tour on www.twitter.com/saddleblaze.
- Alberto Contador