Final answer:
DNA ligase is involved in forming phosphodiester links between DNA fragments during replication but does not proofread DNA; that function is carried out by DNA polymerase, which checks and corrects errors in the newly synthesized DNA.
Step-by-step explanation:
The statement that DNA Ligase can proofread the DNA is FALSE. DNA ligase's primary function is to catalyze the formation of a phosphodiester linkage between the 3'-hydroxyl end of one DNA fragment and the 5' phosphate end of another, particularly in closing the nicks within the Okazaki fragments on the lagging strand during DNA replication.
DNA polymerase I, on the other hand, removes RNA primers from the developing copy of DNA, replacing them with DNA nucleotides. Furthermore, it is DNA polymerase that plays a pivotal role in proofreading DNA. It checks every newly added base and has an exonuclease activity that can correct errors by removing incorrectly paired bases. This proofreading ensures the fidelity of DNA replication, and it is not a role played by DNA ligase.