You are not completely right. Risk-neutral pricing means that the price you'll quote for a given instrument at a given point in time will be the same as the capital you'd require at the same point in time to build a self-financing strategy which will deliver exactly the same future cash flows. The replication mechanism need not be dynamic, it may be static (see for instance static replication of a forward contract by "cash & carry" argument).
This concept is quite intuitive and easy to grasp. However, assuming the existence of a risk-free investment vehicle, best known as the risk-free asset, along with a complete market model defined under a probability measure $\mathbb{P}$, noting that the above claim is strictly equivalent to saying that "any self-financing strategy should emerge as a martingale under a probability measure $\tilde{\mathbb{P}}$ equivalent to $\mathbb{P}$ and associated to the risk-free asset numéraire" is far less intuitive.
There is a lot of theory behind this last statement (see fundamental theorems of asset pricing). I invite you to investigate on your own as this would require a book to answer. But if you want to be convinced, just go back to the binomial model set up and observe how by using a replication argument, one can get rid of historical probabilities and define a new set of probabilities under which discounted asset prices are martingales.
At the end of the day, if you have a complete market model, by absence of arbitrage, there should be a unique risk-neutral measure $\tilde{\mathbb{P}}$ under which:
$$ \frac{V_t}{B_t} \text{ is a } \tilde{\mathbb{P}}\text{-martingale} \tag{1} $$
for any self-financing strategy $V_t$ and $B_t = \exp(\int_0^t r(s) ds)$ the $t$-value of a risk-free cash account in which $1$ unit of currency has been invested at $t=0$.
Applying this in your case:
- Investing in the ZC bond is a self-financing strategy: $V_t \to B(t,T)$
- What you have defined as $D_t$ is the inverse of what we just defined as $B_t$: $B_t \to 1/D(t)$
- Claiming $(1)$ by definition means that, $\forall t$
$$ \frac{V_t}{B_t} = \mathbb{E}^{\tilde{\mathbb{P}}}\left[ \frac{V_T}{B_T} \vert \mathcal{F}_t \right] $$ which using the above notations writes:
$$ B(t,T) D(t) = \mathbb{E}^{\tilde{\mathbb{P}}}\left[ \underbrace{B(T,T)}_{=1} D(T) \vert \mathcal{F}_t \right] $$
hence
$$ B(t,T) = \mathbb{E}^{\tilde{\mathbb{P}}}\left[ 1 e^{-\int_t^T r(s) ds} \right] $$
where the first line is exactly the equality you gave and the second finds the following interpretation: the value of a contingent claim is the expectation of the discounted value of the future cash flows it shall pay, where the discount is performed at the risk-free rate.
