Il Saggiatore (The Assayer) is a polemical text that Galileo Galilei wrote in response to Orazio Grassi (using the pseudonym Sarsi), on the nature of the comets that appeared in 1618.
No, this is not the case. Galluzzi, in the same video, from 32:18 to 32:53, states the following (my loose translation from the Italian):
There is an expression that Galileo uses, that reason does violence to the senses. It is very strong: reason must do violence to the senses. And precisely because of this, he shows enormous admiration for Copernicus and his followers, who made enormous achievements precisely because they were able to do violence to the senses with reason.
Would it be safe to say, that according to Galileo's thinking, that our senses provide us with a 'relative', or 'subjective', view of the universe?
No, this is not the case. Galluzzi, in the same video, from 32:18 to 32:53, states the following (my loose translation from the Italian):
There is an expression that Galileo uses, that reason does violence to the senses. It is very strong: reason must do violence to the senses. And precisely because of this, he shows enormous admiration for Copernicus and his followers, who made enormous achievements precisely because they were able to do violence to the senses with reason.