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But this again still seems wrong to me... I thought fat contained and helped nutrients be absorbed into your body. Or if I'm wrong, then perhaps you could correct me?
No, not really.
Milk is a bit of a special case because its fat is organized in special structures, but even in that case it does not contain or help nutrients being absorbed into the body (aside from fat and a couple of fat-soluble vitamins).
Milk has several sphere-like microaggregations of nutrients, like fat globules and protein micelles (particularly from casein proteins).
The protein ones in particular are what makes cheese a sort of gel and in both skim milk, whole milk or cheese makes protein get absorbed more slowly.
Skim milk still has these, and in fact you get a slower digestion and absorption than the purified proteins and components alone.
But the fat globules themselves are not so important in terms of other nutrients. They do slow down the absorption of fat itself a bit, but their main function is to allow the dispersion and emulsification of fat in milk without aggregation (think of trying to mix oil and water) and prevent self-digestion by milk enzymes (which however is not a problem after pasteurization).
Not only that, but whole milk in stores is generally homogenized anyways, which is the process of breaking up these fat globules. Otherwise in its natural state it would spontaneously start to separate into two layers as a mix of globules and proteins would still aggregate and rise to the top after less than a day.
And skim milk is not made by skimming the top of milk anymore, but by using centrifugation, which is better as it gives a clearer separation of fat from other nutrients (so protein is not really lost this way, aside from trace levels of 0.005 the original ratio).
Basically, the main things you remove to get skim milk are a lot of fat and a couple of very common liposoluble vitamins you can find in most food (A D E K) which are then usually added back just for good measures.
Absorption efficiency and nutrient intakes of other nutrients remains the same, and in a sense it's actually increased 150% if you were to look at percentages by calorie content.
Not having to digest fat can speed up digestion and change how full and satiated you feel, but fat from almost any other source (including EFA etc) will have essentially the same effect in those respects, so again drinking skim milk and using butter (or other milkfat sources like cheese) in the same meal is really not different than just drinking whole milk, but gives you more flexibility in how you prepare your food and balance your diet or make things more palatable to you.
