It’s quite a complicated topic, but yes, this is true. When creams are left open and exposed to open air, this leaves room for pathogens and bacteria to enter, causing your cream to lose its effectivity and oxidise.
There is another side to this – there are product houses that insist on putting their creams in jars that you have to open and close all the time even though the active ingredients in that cream are susceptible to degradation by being exposed to the air. There are other companies that have gone to great lengths to ensure that their products are stabilised and they will use very expensive technology to protect the ingredients inside their creams and choose their ingredients wisely to avoid this.
Other companies take it a step further and create airless pumps and tubes for their products so that every bit of cream is equally active down to the very end of the bottle. This is why most of our professional products now come in airless pump containers, which do not allow air or light to interact with the product, giving you a sterile and active product.