Absolutely not. For land entry, the US has a process by which you are allowed to withdraw your application to enter the country. That is exactly and precisely intended for situations like this.
The mission of Immigration is to block anyone who isn't a genuine "Visitor" -- people who come to the US to
- commit acts of terror or other crime
- seek employ (without a proper visa for that)
- go "on the dole": seek benefit of public services like food stamps, Medicaid, public housing, etc. much of which is provided by the States, but States aren't allowed to run their own immigration services, so it's all on Federal immigration.
- Overstay their visa, or effectively live in the US through repeated visits
A refusal is a big deal. It says there were serious issues with your application that made border authorities worry you would do one of the bullet-point things above. A refusal means future applications will be viewed with distrust.
Further, Canada is a special case for the US: It's a GDP equal, so they're not crashing the gates, and easily half the population is within an hour's drive of the US border. Which means Canadians and foreign visitors to Canada make frivolous, unplanned, on-a-lark visits to the US all the time. Like, for lunch.
This creates a perfect storm for people showing up without proper documents. When this happens, it does not reflect in any way whatsoever on their trustworthiness to not do that above bullet-list of things America is worried about.
So burning a refusal into their immigration record would be completely inappropriate.
That's what "Withdraw your application" is all about. The immigration officer will instruct you "In the future, immigration officers will ask you if you were refused entry into a country. What is happening here is not a refusal. Don't tell immigration officers you were refused entry because of this. We just caught your paperwork problem early, before you applied for entry, so not a refusal. Got it?"
If you did tell US border guards in the future that you were refused, they would probably look in the computer, see the "withdraw", ask you the date and location of the "refusal" and give you a lecture about it not being a refusal and stop saying that. If you tell the UK border guards that you had a US refusal, they'd have no way to check that, and that would prejudice your UK entry.
So, not a refusal.