Above statement is 100% correct. A company is an artificial person created by law. It has not any hand, leg, heart or physical body. Its existence comes when a company is formed and registered under company law. After coming in existence, it can do all business work like a human businessman. It can open his bank account. Company can buy or sell any asset on his own name. Company gets loan on his own name. It can sell own shares in the market.
There will not any effect on the company whether any shareholder will come or go. Company will live even if any shareholder sells his all shares. Other person who will buy the shares, will become the new owner of company. Company will not have any personal relation with shareholder. Every shareholder's liability upto his bought shares.
It has also its own a common seal. This seal will use in all the agreements which will be done on the name of company. Company can not sign, so it is very necessary for making common seal which company can use as showing his identity on every agreement. All the documents will only legal if authorized person's sign will be on the document and company's seal will be on same document.