Actually, the "new guy w 5 posts" was correct, just missed slightly in his terminology.

Liquid dish soaps - like you use in the sink - have no abrasive content.

However, powdered DISHWASHER detergents do use abrasives to assist in the cleaning process. This is why it is not recommended that fine crystal and dishware that have metallic decorations be washed in the machines as it will etch the glass and in many cases remove the metallic trim. Many manufacturers of fine cutlery also state that the abrasives can harm the fine edges on knives. Cheap glassware will gradually get a cloudy look from repeated washings with these products. (But - There are many bio and enzyme based dishwasher detergents that do not use abrasives.)

Regarding scratching the chain . . . . .?

I have heard of people using the dishwasher to clean baseball caps, but using the dishwasher as a degreaser tool - well, every man has to determine his own level of bravery.