We know that EAC (Estimate At Completion) = BAC (Budget At Completion) / CPI (Cost Performance Index)
This means that EAC = BAC when CPI = 1. Let's dig deeper...
We know that CPI = EV (Earned Value) / AC (Actual Cost) . Now since CPI = 1, we know that for EAC to be equal BAC, then we must have EV = AC.
We also know that CPI = BCWP (Budgeted Cost of Work Performed) / ACWP (Actual Cost of Work Performed). And since, again, CPI = 1, then BCWP has to be equal to ACWP.
In conclusion, EAC can be equal to BAC if the budgeted cost of work performed is equal to the actual cost of work performed, in other words, the project is on budget (not a single $ over budget, and not a single $ under budget).
If you think about it, every project starts with EAC equal to BAC, but rare are those that finish that way.