Sheldon Brown was quite right imo.

Aligning the dropouts really isn't going to correct the tire not being centered within the crown.

Firstly, there are two ways to re-center the tire within the crown:

1) The fork blades are both bent to the right or left, moving the wheel in the same direction.

2) The dropout slot is filed deeper to tilt the wheel inone direction or the other.

The first thing to do is determine which approach is appropriate:

Riding the bike (with a smooth headset), does the wheel turn itself to the left or right?
Use one hand, then the other. Can you ride straight by only pushing foreward on one side of the bar or the other? Which side?

If you're pushing foreward with your right hand, the wheel and bike is pulling to the right.

To correct for a rightward pull, the tire contact patch needs to be moved to the right, either by bending both legs to the right, or by filing the right dropout deeper.
Note that tilting the wheel by filing will also move the tire in the opposite direction within the fork crown!
Whichever of those two methods corrects the steering and ALSO centers the tire within the crown, that's the method to use. It's not a matter of being able to simply use the easier (filing) method unless that corrects both issues, and a wrong choice may ruin the fork.

For filing the dropout deeper, you'll need a sharp round file.

For bending the legs, follow these steps:

First measure the space between the fork tips. It should match your hub and is usually 100mm.
Lay the bike on the side you want to move the rim toward. Weight should be borne by pedal, handlebar and saddle, with pads under each point. Rotating the crank to a best position by trial and error will help balance everything when thebending starts.

With hands on the bars and seat post, use one foot to push one dropout toward the floor. It will spring back until you've increased the force beyond a certain level. You will measure the distance between fork tips several times while repeating this, until you achieve 1-3mm of bend movement that holds.
Note that you can recover about 1mm of that bending with a much smaller force in the opposite direction. That's metal stress memory.
You will then do the same to the other leg, until the distance between fork tips again matches the hub's width.
Never try to over-correct, except as a final stress-relieving where you'll bend the leg "back" that 1mm of memory. It's better to ride the bike and test it between efforts, with a periodic re-evaluation of whether it is still better to bend or file your way to a perfect alignment.

Note that this is physical, hard work. Hard on the back when the wheel may have to be re-fitted many times and you'll have to squat down to measure the dropout spacing many, many times. The actual bending borders on gymnastic. You gotta be good, and patience is paramount.
Chainstays are done much the same way, during which the seat stays are nearly ignored. Rear dropouts sometimes need to get filed too. Filing front or rear dropouts is more about correcting a poorly-built frame than fixing a damaged one.
The rewards are that the job gets done, and that the task will get a little easier each time you do it, maybe.
I say maybe because there is a huge variability between frame tubings. Some almost melt, and some are like very stiff springs. I've more or less straightened them all, and at only 158 pounds, I've been challenged by some. Creating a sufficiently-impactful bending load with accuracy can definitely be challenging.

Lastly, you don't want to damage your fork by buckling it or bending it wildly. It takes a solid amount of confidence to do these repairs.
You can experiment on cheap frames, but remember they can be re-bent a whole lot easier than Columbus SL.
You really have to be a little cockey doing frame/fork repair this way, but you can actually do it roadside with no tools using only your wheel hub as a measuring guage. I've done that, not only in emergencies, but as part of getting a vintage bike finely sorted out while also trying to get in a longer ride. Practice makes almost perfect.
Always a bit of risk. I've done well over a hundred, and haven't wrecked one yet. But, I broke a fork tip off the other day by trying to twist out a frozen stem while holding the front wheel between my knees. Cheap Motobecane fork, but took hours to correct in the end, with a UO8 fork, stripped-to-chrome, rethreaded (BSA) and shortened steerer. That bike lives on!

BTW, about half of the used road bikes I buy have alignment issues. Usually it's cheaper ones, easier to bend and treated roughly by previous owners. And some (especially lower end frames)are no doubt made that way.