How true are these claims?

They are very true! The British had three Armies in the Middle East, 8th Army in Egypt, 9th Army in the Levant and Iraq, and 10th Army in Iran. Against this, the Germans and the Italians could muster at best the equivalent of an Army. Logistics were also precarious, with only some supplies capable of being brought in to closer ports like Tobruk, so the bulk of Axis fuel and ammunition had to be transported from Tripoli, all the way into Egypt by truck. It's extremely doubtful that Rommel's forces could have made it to the Suez Canal, let along Iraq, as reinforcements began to reach the British and the 8th Army recovered it's strength at El Alamein.