Person's Financial vs Government Risk Viability

When calulating an individual person's financial risk and viability, we look at his/her debt to income level (DTI), but when talking about a country we always look at debt to GDP.

However, is this valid?

Every dollar government borrows and spends makes the GDP go up.

This is akin to looking at an individual person and counting everything he has purchased with his credit cards as "income".

(Also, the GDP is not the Government's income. It is ours. As soon as the government starts creating something of value and selling it at a profit, it can count it as it's income.)