Tell the landlord that neither of your inexperienced opinions matter very much. Tell him that you are going to call a countertop installer for a professional opinion. Include, if his opinion is that you could not have caused the crack, then he will appear in court to testify to that. Tell him expert witnesses charge in the thousands to appear in court which he would be liable for if you won. So he better have his own costly expert witness to counter yours. Now there will be a lot on the table for him if he loses.
In your favor: Setting hot pans on Corian will discolor it first. IMO, it will not crack it. Also, Corian has been out of style for over 20 years, so I assume your countertop is very old and possibly brittle.
Not in your favor: The crack is near a stove or cooktop. Placing a lot of weight (standing) on that area can crack a countertop.
Get the opinion of a pro installer and then learn how to sue in small claims court. Suing someone sucks, but look at the alternative if he wants to be a harda$$.

