That's one way to view it. The truth about anything real in this world is that it is too complex to have only one valid explanation. Don't fall into the trap to only believe one. Look at the other ones and find that there is more to it than any single explanation can provide.
Money is a reasonable way to track favours, but it's also a reasonable standard exchange medium, it's also a reasonable representation of value, etc. But for all explanations you can also find reasons why it's not, e.g., it's not a favour because a favour is a one-to-one relationship, while money you can get from one person and use it to get something from another person. (No need to counter argue here, you don't need to convince me. I just wanted to present an example of why the idea of "money=favour" is not perfect as well.)
I'm not sure if I get that <government> part. Is that only for the example? If I convince you that I have a cool t-shirt for you, then I give you the t-shirt and you give me the money, not the government, and if I get the money depends mostly on your decision if the t-shirt has value to you or not. There might be cases where I could convince the government that you should give me money, but in the case of the t-shirt that's unlikely.
Using that example can you understand the confusion and explain more in detail? Thanks.
The decision depends upon what value I think the t-shirt has, what value I think the money token has, what value you think the t-shirt has, and what value you think the money token has.
I guess I am thinking of money as being a token of favour against a third party (<government>) not involved in the transaction, and moreover being a token for a favour that will never be invoked.
edit: From this perspective it seems reasonable to ask "what difference does it make what the third-party is?" and "if the favour is never to be invoked, why think of it as a favour at all?".
edit 2: the "favour" and the "value" here are quite different ideas, if that part is confusing.
Money is a reasonable way to track favours, but it's also a reasonable standard exchange medium, it's also a reasonable representation of value, etc. But for all explanations you can also find reasons why it's not, e.g., it's not a favour because a favour is a one-to-one relationship, while money you can get from one person and use it to get something from another person. (No need to counter argue here, you don't need to convince me. I just wanted to present an example of why the idea of "money=favour" is not perfect as well.)