I don't dispute that. AFAIK all the British Empire and Commonwealth (BEC) troops were better trained than the Italians. The problem in June 1940 was that there weren't enough of them.Hobart's mobile division had spent the last year training for an Italian invasion.
However, the quality of their equipment wasn't that superior to the Italians at this stage, because AFIAK the BEC forces in the Middle East in June 1940 were still using a lot of World War One era equipment, including their artillery.
The 7th Armoured Division was reputed to be the best trained of all the BEC formations in the Middle East in June 1940. However, it wasn't up to full strength in June 1940 and would not be until September when the first reinforcements arrived. It was the same for all the BEC divisions in the Middle East. This is the relevant paragraph from the British official history.
AFAIK all the British tanks in the Middle East in June 1940 were Light Tank Mk VI, which I admit was still better than the Italian L3. AFAIK the British didn't have any cruiser and infantry tanks in the theatre until September 1940.In Egypt General Wavell had some 36,000 men; they were not however organized in complete formations. Equipment was seriously short throughout, especially artillery of all natures, ammunition, fighting vehicles, and transport. The two armoured brigades of the 7th Armoured Division had each two regiments, instead of three, and these were only partly equipped.6 The 4th Indian Division also had but two brigades and part of its artillery. Of the New Zealand Division there was as yet one infantry brigade, a cavalry regiment less a squadron, a machine-gun battalion, and a field regiment of artillery. There were also fourteen battalions of British infantry and two artillery regiments. There was, in addition, the Egyptian Army, which was in some respects better equipped than many of the British units; but as Egypt had not declared war on Germany the amount of support to be counted on from the Egyptian Army was doubtful. In Palestine there were about 27,500 troops consisting of an in-complete horsed cavalry division, two cavalry regiments, two Australian brigades with two field regiments of artillery and some divisional troops, and a British infantry brigade and two other battalions. Of these troops the cavalry and the Australians were unlikely to be fully equipped and trained before the end of the year. From Palestine one brigade might have to be provided for service in Iraq, while certain other units were earmarked for internal security duties.