The answer to that question is yes. As long as Israel accept welfare payments from the American taxpayer, it is now right to whine about being a “vassal state.” When it proudly rejects such welfare, however, it can claim that right.
In theory you are correct — the US Aid to Israel was 2.5 Billion in 2009 -— 75% of which was subsidies to purchase or develop US weapons, so most of this money stays domestically in the USA and significantly decreases the “unit” costs of American weapons, as the USA buys these same weapons and the sales keep USA cost down.
It’s a significant help to Israel, still, to put the size of the aid in perspective, the USA gives Eqypt $1.7 billion and Jordan $.6 billion per year, $.6 billion to the “Palestinian authority” etc.
In short, the USA aid to Israel is about the same as the USA gives to terrorist nations.
Given Israel’s strategic role in the middle east, it is also money well spent. Certainly cheaper than an air-craft carrier fleet.