'Hello, how are you? From China? Do you need a guide?" asked the Cuban man, who obviously saw us as a potentially lucrative diversion from his date with his girlfriend when he sidled up to us.
Naturally, we declined.
Which was when he fired his parting salvo.
"Are you sure? You'd better be careful! There are spies all around. Out of 10 Cubans, seven will be spies!" he cackled as he walked off; miffed, no doubt.
That was the most intriguing statement we'd heard in our 10 days in Cuba, in a trip that was mostly led by a perfectly pleasant local female guide - as we travelled from Havana all the way east to Santiago de Cuba.
We were back in Havana, however, with two days to explore the old city.
Perhaps it was the area we were in that inspired this talk of spies: we had just left the Revolutionary Museum, and were walking towards a collection of military exhibits in a park. At the Granma Museum, there's a Hawker Sea Fury F50 plane mounted in the centre of a gigantic glass building.
That's the plane which helped repel the seminal Bay of Pigs invasion in 1961.
Next to it was the engine of the Lockheed U-2 spy plane which was shot down above Cuba during the Cuban Missile Crisis in 1962.
Then, a model of the said weapon of destruction - the SA-2 Guideline surface-to-air missile.
Spies? Oh yes, it was quite believable, from what we had heard over the first few days.
Like good ol' Communist China, there's also a system of governance where Cubans can't move around of their own accord.
If they live in one town, for instance, they need official permission to move to Havana, or to any other town as they'll be monitored by the "neighbourhood watch" people who notice who's new and over-staying in town.
On our second last day in Cuba - having experienced the Unesco heritage site of Trinidad with its filigreed and colourful French architecture, the blue Caribbean seaside resorts, the quaint Spanish-influenced, sugar crop-driven towns of Sancti Spiritus and Camaguay and Santiago de Cuba, the place where the revolution started in the 1950s - our interest in Cuban political history was ignited.
The Revolutionary and Granma Museums provide good insights into Cuba's psyche - in this country full of "Che Guevara-isms" (revolutionary sayings by the rebel fighter stencilled and sprayed on the faded walls, along with his beloved dashing likeness) and vintage cars.
Those, along with the faded grandeur of neo-classical buildings, speak most eloquently and romantically of a country that's been caught in a time warp since the 1950s.
Even so, it seems that Cuba is on the cusp of change.