Is Mankiw's analysis of "crowding out" plausible? Or is the entire notion of a demand-and-supply model of a market for loanable funds model workable at all?

I’m getting ready to teach an MBA-level economics course for entering students who have not had an intro economics sequence as undergraduates (or at least not recently enough).  In the course of doing that, I’m actually reading Greg Mankiw’s introductory economics textbooks (I never used it before).  And in reading it, I have come to a conclusion about the entire discussion of “crowding out” as it appears in his—if not other—economics textbook. 

I won’t quote Mankiw’s entire discussion of “crowding out” in his chapter on “Savings, Investment, and the Financial System,” because it’s way too long.  But it is somewhat odd. He looks at what happens when governments begin to run (or to run larger) budget deficits, in the context of a fairly (perhaps too) simple model of a market for loanable funds:

First, which curve shifts [the demand curve for loanable funds or the supply curve of loanable funds--DAC] when the government starts running a budget deficit?  Recall that national saving…is composed of private saving and public saving.  A change in the government budget balance represents a change in public saving and, thereby, in the supply of loanable funds.  Because the budget deficit does not influence the amount that households and firms [my emphasis] want to borrow…it does not alter the demand for loanable funds.

Mankiw’s conclusion (Figure 4 in Chapter 26 of his textbook shows the result)—an increase in market interest rates and a reduction in the quantity of funds borrowed and lent.  I find this odd.  Governments now run a (larger?) deficit.  To finance that deficit governments have to borrow (more?).  With no change in the amount that households and businesses want to borrow, how can adding additional government borrowing lead to a reduction in borrowing? 

Or suppose we alter his argument slightly.  Suppose I wrote:

Which curve shifts when the household sector starts running a budget deficit (i.e., household consumption spending now exceeds household disposable income)?  This represents a change in private saving, and, thereby, in the supply of loanable funds.  Because the household budget deficit does not influence the amount that firms and governments want to borrow, it does not alter the demand for loanable funds.

Isn’t this exactly the same situation that Mankiw describes, but from the point of view of a different (set of) actor(s) in the economy?  It seems to me that, in Mankiw’s terms, it’s hard to see how the demand curve for loanable funds could shift.  I suppose we could resolve this, empirically, by asking whether the total of household plus business plus government borrowing rises or falls in these cases,

I suspect the problem is similar to the problem that many have with the aggregate demand-aggregate supply model (a problem I still have not resolved for myself:  The demand curve is not independent of the supply curve.  In the market for loanable funds, the household sector, the business sector, and the government sector are actors on both sides of the market—they are all both potential lenders and potential borrowers.  When that is the case, a simple supply-and-demand model becomes inadequate to explain the issue involved, and something different, and perhaps more complex, will be needed.