No, that is what you have been told by a salesman, which is to say a professional liar.
Glass bottles: wash it with soap and hot water, at a cost to you and to the environment, and put it outside in a bin that was made at an environmental cost.
Then a huge diesel truck, built and operated at an enormous environmental cost picks it up on it's basically empty trip around the city -I say basically empty because recycling is bulky but light- and drops it off at the depot, where once no one is looking, they put it back in the garbage stream because there is not , and may never be, a market for used glass bottles, and then it goes in the landfill at a much much higher environmental cost than if it was just thrown out honestly.
Some plastics are recyclable, but many are not, and if they contaminate the first bunch even slightly, it turns it into a pile of garbage that has a much higher environmental cost than if it was just burned. Metals are totally recyclable, but we've been recycling them for thousands of years. Cardboard is good, but the environmental cost of cleaning used pizza boxes is higher than the cost of making new ones. Is it more important to harm the environment more while paying higher taxes, while agreeing to pretend to be doing good, or is it more important to protect the environment in reality?