The Germans never provided autoblindi (armored cars) to the Italians. The equipment transfers/purcahses that did happen were fairly rare. The JU 87s, the 88s, the limited equipment for the d. cor. «M», etc. all happened after serious negotiations. The Germans aggressively forced the return of any damaged German equipment salvaged by the R.E. Remember that Germany was trying to equipment their own forces. There wasn't much to spare.
Doctrine was another issue. The Italians viewed the corps as the main tactical maneuver element, not the division. So initial efforts were for a corps-level recce unit.
Finally Italian industry didn't wish to lose business due to Germany supplying equipment to the R.E. that they wanted to provide. The AB 40-43 series were quite capable, so production was the main problem.
In terms of borrowing, no. The Germans were always loath to put any German units under Italian command.
Pista! Jeff