No, you are taking out a mortgage on a depreciating asset and investing cash at your level of risk tolerance. If your level of risk tolerance is a savings account at 0.5% so you can always have an emergency buffer, that's fine.
The argument is that to make an apples-to-apples comparison of total cost of ownership of one car and another, you should always include financing costs. They are basically your lowest cost of capital. Think of it this way: even if you're going to pay cash, leaving the finance cost in allows you some basis of comparision between the cost to you of putting say, $30K cash into a car versus putting $20K cash in. It's not exact but it's a useful simplification.
I will never understand this logic. You do realize that this is investing on margin just with better conditions? At this point we are assuming that you already have an emergency buffer and no financial difficulty whatsoever.
The reason why you should always finance your car even if your income is low is that you can build an emergency buffer that you can use on anything. If you have $30k in your bank account and buy a $27k car then you are only left with 3k. Any potential financial problems will force you to find a loan that very day. If your monthly payment is $500 your emergency buffer will last for years. If you invest that money you will have to compensate for any losses during that time frame by having enough income, it's as if you had $0 savings to begin with.