Gap in coverage after qualifying life event of leaving my job??

Hi all. I’m frustrated and can’t decide if this is because my spouse’s employer is wrong, or if I just don’t know how things work. I left my job on August 12, where I carried our family’s health insurance. Way in advance of this, my husband started setting up plans to enroll us through his company, as my leaving my job is a qualifying life event due to loss of coverage. We provided the relevant dates- term date for insurance 8/13, then there’s verbiage there that “however, your coverage is extended for 31 days after that date.”

So, our last day of insurance coverage will be Sept 14. My husband’s employer says the earliest they are able to enroll our family is the first of the month following our insurance termination- that being Oct 1. They recommend COBRA for the interim, which I’m obviously familiar with. However, is that truly just the way it is?? With all the notice and appropriate forms we’ve given them, they are still able to leave us with an uncovered two week period, and suggest COBRA? Seems like there must be rules around how qualifying life events work that are supposed to preclude gaps in insurance, but maybe that’s just wishful thinking on my part? Thanks!!