Especially as they got a 6 month stamp on their passports only a week ago. They were planning to stay in/around the UK for a month or so.
The problem with the 6-month stamp is that it's only single-entry. The 6-month leave to enter is cancelled the minute they leave the UK and they have to apply for another 6-month stamp every time they come back in again... and the immigration officer is under no obligation to let them back in if they are concerned they may be an overstay risk.
In order to show they are not an overstay risk, they have to be able to prove the following:
- a return ticket (to show they will leave within 6 months)
- enough money to support themselves for the length of their trip (so they won't have to resort to illegal working to survive)
- evidence of ties to return to in their home country (a job, a home etc.), to show they have a reason to go back to the US and won't attempt to stay in the UK illegally.
If they had not gone to Paris (or left the UK for any other country and then tried to come back), their original 6-month stamp would still be valid and they wouldn't have any issues with UK immigration. Unfortunately, because they left, their 6-month visitor visa got cancelled and they had to start from square one to get back in the UK again.
If, however, you apply for a visitor visa in advance, you get a multiple-entry visa sticker and can come and go from the UK as often as you like within the 6 months.
Good old Brexit!
It has absolutely nothing to do with Brexit, I'm afraid. The immigration rules have been this way for a number of years. The UK is not part of the Schengen Zone and therefore there are immigration checks going in and out of the UK/other EU countries. Every time they leave the UK and come back, they need a new visitor visa. The only exception is travelling between the UK and Ireland as they are both part of the CTA (Common Travel Area) and there are no immigration controls between the two countries.