Maybe. They say "... tick must be attached for 36 to 48 hours or more before the Lyme disease bacterium can be transmitted. If you remove a tick quickly (within 24 hours), you can greatly reduce your chances of getting Lyme disease."

https://www.cdc.gov/lyme/transmission/index.html

The article that you reference says that rash takes 3 days to develop, she feels discomfort from the bite almost immediately and the site gets visibly inflamed in less than 3 hours. So I think it is a reaction to the saliva of the tick. We would almost certainly remove it in less than 12. We probably have had that bacterium at some point but we haven't had any of the other symptoms, the characteristic "bullseye" rash, etc. If we ran to the doctor every time we got bit by a tick we'd be on antibiotics for 4 months of the year and certainly suffering from intestinal dysbiosis all the time.

We know a lot of people who've gotten it and are very aware. The thing about Lyme is that it has certain characteristics that make it very compelling to hypochondriacs and about 20 years before the real Lyme epidemic there was an epidemic of people who thought they had Lyme disease so it is a real mess.