This was true for a long time. Now the rules have changed slightly. Whether you need to look wealthy or not depends on how you make money. If you do business where your partners see you, it is important that you look and dress the part.
As a manager, you should dress appropriately when dealing with other people. There are some generally accepted exceptions like IT industry. When two IT guys are dealing face to face and they both do not care about dress code, it is acceptable not to wear conventional business clothes. But when the same IT guy needs to visit the bank to get a loan, he should wear business clothes.
You have to make good first impression on people who will influence whether or not you will get your loan. There are people who work only through internet and communicate through e-mail or chat.
You can manage results of your team through internet and also get your loan approved without visiting bank in person. If nobody sees you, it is not important how you look, right?
No. It is not complete truth. There is always one person who does see you. He is always watching. Clothes you wear influence your self-image. Even if you work from home, it is good idea to change your clothes during your working hours. This will help you to switch to ‘working mode’ and back.