I'm not an expert, but any time I see oil in a canning recipe I get nervous...and any time I see a "canning" recipe without any processing, I get even more nervous! My impression is that this recipe doesn't look safe. Maybe if you put it in the fridge...but I certainly wouldn't sit it on the shelf and think that the float of oil is "preserving" your peppers.

This is a safe recipe to use, no oil. Even storing in the fridge with the oil could be a problem with a risk for botulism if stored for more than a few days to a week. Not safe at all in the cupboard. If you want, you can use dried oregano in it. :
Colorado Mix (Pickled Pepper Vegetable Blend)
2 1/2 pounds peppers, mild or hot as desired
1 pound cucumbers, cut into 1/2-inch chunks
2 to 4 carrots, cut into 1/2-inch chunks
1/2 pound cauliflower, cut into 1-inch flowerettes
1 cup peeled pickling onions
7 to 14 garlic cloves, as desired
6 cups vinegar
3 cups water
2 tablespoons pickling salt
2 tablespoons sugar, if desired
Yield: Makes 7 to 8 pints

Procedure: Wash and prepare vegetables. Slit small peppers. Core large peppers and cut into strips. Remove blossom end of cucumbers and cut into chunks. Peel and chunk carrots. Break cauliflower into flowerettes. Pack vegetable medley into hot, sterilized jars, leaving 1/2-inch headspace. In 3-quart saucepan, bring vinegar, water, salt and sugar to a boil. Pour hot solution over mix in jars, leaving 1/4-inch headspace. Remove air bubbles. Add liquid to bring headspace to 1/4 inch. Wipe jar rims. Add pretreated lids and process in boiling water bath. For best flavor, store jars five to six weeks before opening.

Table 1: Recommended process time for Colorado mix in a boiling water canner.
Style of pack/Jar size Process time at altitudes of:
6,000 ft or less Above 6,000 ft
Raw:
Half-pints or pints 10 min.

Quarts 15 min.