401K loans aren't double taxed, per se, because loans aren't.
Loans are not income generally
What they're overlooking is that when you take a loan, that's not income so you are not taxed on it. Wait, how does that work? How is it not income? It's cash in hand! Well, that's a "cash" way of thinking, and in big accounting, it works that way on the cash flow statement.
However, the IRS taxes people on their income statement. That counts both cash gained and liabilities indebted. So you have +$10,000 cash because of -$10,000 debt you now owe. These two cancel each other out, and you have $0 net income that you have to pay taxes on.
If there's some sort of bonus, e.g. you borrow $10,000 but as a promotion they only require you to pay back $9900, then yeah, that $100 is income. Likewise if you default, the unpaid debt is considered income, but that gets weird.
But 401K loans can result in a kind of double taxation
Now, with a 401K, if you leave the job you must pay the loan back very soon. If you can't, you are forced to make a premature withdrawal from the 401K to settle the loan. That means you need to pay normal income tax on the 401K money (because you never did at time of contribution) and also a 10% premature-withdrawal penalty.
So it's tax + 10% more, not quite a double tax depending on your bracket.
Going onto the unemployment line, does that feel like a great time to repay a large loan? Chuckle, I didn't think so. So usually, the above situation is forced upon you, meaning you accrue a whole bunch of taxes (normal income tax + the 10% penalty) right when you can least afford it. Ouch.
Worse, 401Ks are for retirement. When you default on a 401K loan, you irrevocably rip a chunk out of your retirement savings, and you will have less in retirement. There's no "catch-up" contribution limit to let you regain your lost ground.
Lastly asset protection. 401K investments are fully protected from lawsuit and bankruptcy. If you default on credit cards, the 401K remains intact. From an asset protection POV, you're better off taking the credit report burn and keeping the 401K intact for its purpose: retirement.
For those who think asset protection is cheating creditors, not at all. It just prevents creditors from using force on you. You can always choose to pay it off. Pay minimums, subminimums, or zero until able; each has different effects. Only bankruptcy prevents paying it off later, so don't! I am not recommending bankruptcy, merely noting 401Ks are protected.