The solution in the memo is a mathematical solution that you need to think about from a less-intuitive angle. Remember that we are dealing with a timeline of cashflows and all we are trying to estimate is a level amount of cashflows that end n years after death.
We know that the annuity has a minimum of n years so we start there. We then are just, separately, adding the annuity till the policyholder dies and we are ordering the guaranteed annuity to happen first to simplify the calculation.
The key point you need to remember is that whilst the cashflows of the complete life annuity are being discounted by more than we expect, the ages remain the same which is why this works (in a less-intuitive way).
Where your answer wouldn't be correct is that you still need to take the expectation of the expression you have. V^t and a^(bar)_t are random variables, not an answer so you would need to take the expectation of your expression which would result in your answer which would be accepted.
The problem with your answer is that now how will you get the variance of your expression? It'll be much more challenging and time-consuming which is why the memo went down the route that it did (making the next steps much easier).