I changed wheels and tires from training level tubulars to clinchers 30 years ago. Took a corner not as fast as I did routinely in the wet on the tubulars. As I approached the apex, it was "oh s***, I'm not going to make it" except mot as polite and a lot louder. Both tires slid out and I came down hard.
This was just good, clean water on a corner I had taken wet many times. (My regular winter ride in Seattle.) Yes, tire changes can matter a lot. I am not an expert on gravel but I have noticed big differences in road tire grip that is obviously mostly a matter of thread compound. I now pick tire based in large part on their grip. I've had really grippy tires bail me out when I've started to slide on gravel and the like, then re-grip when they came to good pavement.
Ben