Then I don't think that you grasp the concept of saving your $1's and $5's. No one is "borrowing from Peter" in order to put money in savings. They are simply applying a different method than you.
Let's say that Mrs. X has budgeted that same $200 for her weekly spending that you used in your example. At the end of the week, when she needs bread, milk, apples and eggs but only has $10 to cover it, she doesn't go to the ATM to take out $20. She uses $11 from the pile of $1's and $5's that she accumulated over the week. In the end, she only saved $2 in her jar at home. But it's still $2 saved, which is more than some people manage to put aside each week.
Your example stated that Mrs. X would have taken the original $200 from savings, as was the subsequent $20. That may be the way that you handle your finances. We have savings accounts, money markets and investment accounts for saving. That's why I asked if you were in the habit of using money from your savings account to pay for your living expenses.
We use the checking account to handle everyday expenses. I don't take money out of savings unless it is for the purpose for which it was set aside...home improvements, new vehicles, vacations, emergencies. Money for the daily living would be pulled from the checking account. If I under-budgeted for the week's groceries, it wouldn't come out of the fund for new windows. It would be taken from the weekly spending money and we just wouldn't go out for pizza that week.
In the long run, I really don't care how other people save. If it works for them and they manage to meet their goals, then more power to them. I have a regular savings plan that puts money into each account on a regular basis. The money gets moved automatically and I never miss it. The method works for me. But I also don't live so close to the edge with my finances that I don't have enough cash in my wallet at the end of the week to pay for a small bag of groceries.