Actually, you would be incorrect. Here is how the warranty is stated on Columbia's website:
LIMITED WARRANTY - OUTERWEAR
(DOES NOT APPLY TO FOOTWEAR OR SPORTSWEAR)
SEND YOUR CLAIM USING A TRACKABLE SHIPPING METHOD
What This Warranty Covers. This Limited Warranty covers defects in materials and workmanship in outerwear manufactured by Columbia Sportswear Company (Outerwear). This includes defects in zipper pulls, zippers, snaps, stitching, dye bleeding, leaking of Columbia's waterproof Outerwear line, and any other Outerwear defects that may occur under normal wear. Columbia does not warranty and is not responsible for damages caused by misuse, abuse, accidents, the natural breakdown of materials over time, or problems that may be reasonably expected with normal wear or failure to follow Outerwear care instructions.
How Long This Warranty Lasts. This Warranty lasts for as long as you, the original purchaser, own the Outerwear. Coverage ends if you sell or transfer the Outerwear.
How To Get Warranty Service. You may seek resolution directly through the retailer where you purchased the Outerwear. In many cases, the retailer will be able to assist you. You may also send Outerwear (including any shell, liner, and other components), shipping prepaid, (you pay to ship the item to us, we pay to ship the item back to you) directly to us.
The OP is lucky that Columbia replaced the coat, but they were not under any obligation to do so.