If the oil filter is loose, you'll be spraying oil all over the place and quickly emptying the pan of all oil.
Do you change your own oil, or use one of the jiffy-types of places? It's possible they didn't take much care removing the old filter, and/or some oil splattered when it was changed. Mobil1 has a tendency to stick to surfaces and drip for months.
We just got one of these trucks, so I'm still learning it. I did notice some oil dripping from the sway bar, which is directly below the filter and oil drain plug, so I wrote it off to stuff that hasn't been cleaned after the last oil change so I'm still checking. Hopefully I won't find some problem with our new-to-us Tahoe. It's otherwise in very good shape.