No.. most people assume insulin is t1... but as you say both can have insulin
T1 can technically eat what they want but really the same is not true for t2's... t2s are insulin resistant and t2 is generally considered progressive
By eating what you want and controlling it with insulin will firstly make you increase weight.. the effects of the carbs and weight etc will more than likely make the insulin resistance worse meaning more and more insulin to the point some people take many hundreds of units a day
The best way is to remain on a strick carb controlled diet to try and minimise insulin usage
The 'can eat anything" still isn't totally true for t1s in the fact that if you over eat and control it with insulin you'll still gain weight and possibly become insulin resistant.... so 'anything in moderation'