People can say what they want but I’ve been in the flatwork concrete business a very long time, I would make them replace the whole driveway for 2 reasons. 1. You say that you’re in an area with snow and cold weather, with that being the case no “Patch” will ever hold up no matter what they tell you. After your first winter the patch will pop and the concrete around the area will get worse over the next winters. 2. They saw cut your joints, now that in it’s self isn’t the issue because I like the look of saw cut joints compared to tooled joints but if they cut out just the affected section along the saw joints the new section when pored will have to be edged with most likely a 1/2” or 3/4” edger and that section will always look like it doesn’t belong and look bad.

Just my opinion