Really? With the USSR supplying Egypt & Syria, the US resupply was crucial. Where did you get that? That was really off the wall.
First, let me note again Nixon's actions were courageous.
The Soviet issue wasn't supplies, there were reports of Soviet troops in the air, the first wave, which were turned back in the face of Nixon's worldwide defense condition escalation. Haven't a clue if they were in the air, but there were several, reports are 6 or 7, Soviet airborne divisions prepared to intervene. They backed down.
The supply issue, certainly important, one of the major issues Israel confronted in the post-war inquiries, they always do that over there. Fired a few Generals over that war.
Sharon describes the resupply as an important factor mentally, it convinced Israelis, and the world America was committed. He also contends that in terms of most critical supplies, ammunition, Israel was at 60%-75%, the only real shortage being 175mm artillery. Peacetime ammunition dumps were emptied, but largely because of Israel's tactical policy of moving ammunition to forward facilities.
That's not to minimize Nixon's actions, but the most important was facing down the Soviets who were prepared to enter the war.