If the marital status on a paystub is "married" and 1 allowance is claimed, does that mean it's at the "married at single" rate, or could it still be the "married" rate?

Married with 1 allowance does not mean your withholdings are at the single rate. If it says married your withholdings are at a married rate. 

The allowances withhold more or less taxes within that married rate. The more allowances you have the less taxes are withheld from your check. So 1 allowance would withhold a higher amount of taxes. 

Ok, when someone selects "married but withhold at higher single rate" on their W4, how does that appear on a check stub compared to "single" or just "married" ?

I believe it should say "married but withhold at higher single rate"but you may want to double check with your HR to confirm. It is perfectly acceptable to indicate on your W4 to withhold as Single if you wish.  And with no exemptions, either, if you want, and still file your income tax with your actual married status.  People often do this to try to be sure that enough is withheld. Your W-4 only affects how much money your employer withholds in taxes from your pay.  It does not control your choices as to filing your tax return.