Should Analytic Account be on the Vendor Bill from auto generated Purchase Order?

I only just realised this now, but thought this is strange, can anyone share some lights?

Using V14 Enterprise (yes we'll be upgrading soon).

Step 1. Created Sales Order Quote $600 with a Project/Analytic Account

Step 2. Confirmed the Sales Order $600, auto generated Purchase Order -$500

Step 3. Auto generated Purchase Order inherits the Project/Analytic Account from the Sales Order -$500

Step 4. Created a Bill for that Purchase Order, also inherts the Project/Analytic Account in the journal -$500

Step 5. Created an Invoice for the Sales Order, inherts the Project/Analytic Account in the journa. $600

Stpe 6, when checking Analytic Account report, I got the following:

Invoice $-500

Invoice $600

Bill $-500

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Balance, $-400

It seems the Bill or Cost of the purchase order gets doubled when we record the bill with the analytic account, and during the invoice when the system also captures the cost.

Should we not assign an analytic account on the bill?