> All modern engines are fuel injected, so the intake valve only ever sees filtered air.

Not even close.

There's two sources I can think of off the top of my head for contamination of the intake valves. Others have mentioned the exhaust gate recirculuation, but there's also crank case air that can be recirculated.

A cold engine's piston rings don't fully seal properly against the cylinder walls. They can't or else the piston could drag and scrape the wall when thermal expansion occurs. So when you start a cold engine, a great deal of pressure slips past the rings into the crank case where the engine oil is. Depending on what phase the escape occurs, it can carry gasoline, combustion gasses, etc into the crank case.

In the bad old days when emission regulations weren't a thing, the normal practice was just to let this blow by vent from the engine crank case into the atmosphere. The EPA at some point considered this not so good, and mandated that this needed to stop. The solution that was implemented was to recirculate the air from the crank case into the intake manifold. Unfortunately this means that any particulate is also recirculated as well (evaporated oil is the nasty one) and can gum up the intake valves.

Now what you're thinking about is gasoline direct injection engines, and top tier gasoline isn't going to clean the intake valves because the gasoline is injected direct into the combustion chamber. But there's still port injected engines which are still fairly common, which wash the gasoline over the intake valve and in turn wash the contaminants from blow off the valves and into the combustion chamber. Hence why Top Tier gasoline is beneficial to engines that use valve injection.

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Just a fun aside for anyone that runs a gas car; if you've ever wondered why oil change intervals are either have both a time based and a mileage based interval; it's because of that cold engine start blow by. Oil doesn't degrade sitting in an engine case, but it's performance does degrade when gasoline from a cold engine being started slips past the piston rings and mixed with the oil.

When you're running long miles, it doesn't matter as much. The engine is able to get up to full temperature, which both properly seals the piston rings, but also warms up the oil, which causes the gasoline that has gotten into the oil to evaporate and be circulated back out.

But that doesn't happen if the engine isn't run long enough to get up to temperature; if you're making short little 5 minute trip commutes every day, then the oil just keep getting contaminated more and more with gasoline. Left unchecked, the oil ceases to be able to properly lubricate the engine from the contamination, and heavy wear and tear starts occurring in the engine itself.

A proper oil change interval would take into account all the factors that effect oil life; the engine's temperature when it was started, how long the engine was run, how hard the engine is run at, etc to calculate how badly the oil has been contaminated by cold starts. For people that have an oil life monitoring system; that's exactly what it does. But what about everyone else? Do you expect people to note down the ambient temperature, and the engine temperature every time they start up the car, plug it into an excel sheet and see how much oil life is left?

Hence the need for a simple formula that could accommodate most use cases; the 3500 mile or 6 month interval. 3500 miles for people that were running their cars hard such as towing boats, RV's, etc, which wore the oil out faster then normal commuters, and 6 months for people that were just making a 5 minute commute by car every day while in the middle of winter.