False. Sights observed through a telescope were also part of "what they saw around them." A true theory accounts for all the evidence (and if it's not ultimately reducible to or based on something you can get from the five senses, it's not evidence).
Telescopes also show that Jupiter's satellites experience eclipses, which isn't direct heliocentric evidence, but does tell you that Jupiter and its moons shine by reflected sunlight rather than intrinsic luminosity.
Telescopes also show sunspots, leading towards the discovery that the Sun is an active body, and to some notion of its size and mass. Telescopes can also show Venus transiting the Sun giving you a great idea of their sizes, which happened in 1639. http://en.wikipedia.org/wiki/Transit_of_Venus#First_scientif...
The switch to heliocentrism didn't happen overnight or as the result of a single observation or event, but telescopes brought in many different streams of evidence for it.
But, I guess your question was, how did we learn about the structure of the solar system, planets and orbits and all...
By observing the planets, you can map out their path, and you can see that they are not orbiting earth. The only sensible explanation is that all the planets, including Earth, must be orbiting the Sun.
Kepler then further observed that the orbits are elliptical, and then postulated Kepler's laws (that planets orbit the sun in an ellipse, with the sun in one of the focuses).
Historical brainfart.
My guess, is that here he is talking about undecidability which appears quite often in mathematical problems, maybe something like this http://en.wikipedia.org/wiki/Wang_tile or http://www.nd.edu/~svandend/Tilings.pdf (pdf).
That's why Penrose is unable to argue against QM the way he argues against string theory: there's experimental evidence and he can't gainsay that.
I think my least favorite line was probably this: "The trouble is, what can you do with it? Nothing. You want a physical theory that describes the world that we see around us." If you're going to use that to reject theories about the reality of the wave function, astronomers in the Renaissance would have been equally justified in rejecting the heliocentric system on account of it being at odds with what they saw around them, or Greek astronomers rejecting the notion that the world was round.