How long must your passport be valid to enter the UK as a vistor?

Hello all!  My baby sister has booked a last minute flight to visit me.  She's aware that her passport expires in Jan 2016.  This morning I got an email that she's gone ahead and booked her flight for 12 days in 11th Aug to 23rd Aug 2015.  I believe her passport expires 18th Jan 2016.  Both her entry and exit flight are booked and paid for so she knows her exact arrival and departure dates.

I'm concerned because her passport has less than 6 months on it.  She's not because she found this guidance: https://www.gov.uk/uk-border-control

Anyone have any experience or words of wisdom?  There's now no time for her to renew her US passport.  http://travel.state.gov/content/passports/english/passports/renew.html  She has a very clean immigration history, several visits, about once every 18 months to the UK to see me for 1 - 4 weeks during each visit for the 9 years I've lived here.

Some countries do have a >6-month rule; the UK does not. The first sentence in the guidance is the relevant one - the PP must be valid for the length of her stay, which it will be. Because it expires in <6 months, she (likely) won't get the standard 6-month visitor stamp.

Thanks!  My sister researched it and I know if I were an outsider I'd be calm and rational about this, but being involved I just panicked because I don't want them to turn her away.