That is, I'm sorry to say, totally wrong.
This goes back to the confusion between analogue and digital technology. In the analogue domain, a smaller "sensor", that is: the film, means a greater degree of enlargement for a given print size. In that situation, your statement is correct.
In the digital domain, however, the image is recorded via a grid of pixels. If there are 20 million pixels on a 1/2.3" sensor and 20 million pixels on a 1" sensor then the same number of points will be delivered to the display medium, be it a laser print or a screen display. The amount of data retained in the display is entirely dependent on the display system. If a 20 million pixel 36mm x 24mm is the recording mechanism, the number of points will again be the same as with the smaller sensors.
As I mentioned above: the main difference introduced by sensor size is the number of photons collected in the pit of each pixel. This will affect the differentiation between each point and therefor the subtlety of differentiation between lines. The bigger the pits, therefor, the sharper the lines will be, again dependent on the display mechanism. However, with the rapid improvement in both hardware and software, the difference between sensors of different sizes has been reduced to a marked degree.