I think you can outsource UI design, but not the UX (if you're a web company).
If you're a company whose value isn't in the website, e.g., a daycare, then I think you can often simply steal the UX from others who have done it in your industry and done a good job.
You always have to think about UX. Just because the web isn't your domain doesn't mean its not important. I'm sure we've all been to websites that look dated and are poorly written, which turned you off from the company.
My point though is subtler, which is that if your value isn't in the web then you merely need to be competitive on the web, and in most of these cases an outsourced UI/UX will be superior than many of your competitors.
If you're a company whose value isn't in the website, e.g., a daycare, then I think you can often simply steal the UX from others who have done it in your industry and done a good job.