Annual US military aid to Israel is around $3-4 Billion/yr. Israel uses the money to buy US weapons. So yes, technically you're correct, Israel purchases most of these weapons - with money given to Israel as aid.
Not all weapons provided by the US are 'purchased' in this manner. Some are given/donated or provided under various stipulations (i.e. Israel assists with R&D or testing)
Obviously, this is just a portion (around 12%) of Israel's defense budget, so Israel does use its own money to purchase weapons as well.
But $3-4 billion in cash 'gifted' by US Taxpayers to spend on US weapons is a decent chunk of change
See: