Avoiding double tax on 401k loan interest?

If you take out a 401k loan, it is commonly said that your 401k loan interest (paid to yourself) is double taxed. If instead of leaving the money in your 401k you roll the after-tax loan repayment and interest repayment into a Roth IRA, do you avoid the second tax? Since my plan only seems to keep track of pre-tax, Roth, and after-tax values and since you can roll after-tax and Roth into an IRA without paying any taxes, I don't see anything preventing you from avoiding the double tax on 401k loan interest this way, but I've never seen this discussed anywhere online.