SDI Solo. Never had the cert question.
More common problem is having a dive op not knowing their own solo policies. One dive op on Curacao that specifically has a solo diving policy on their website and who I had solo dived with before told me on my last trip that they don't permit solo diving. My response was yes you do. Their response was no we dont and never have. My response yes you do, I did on my trip last year with you and it is specifically allowed on your website. The employee had to look it up. After a few minutes and a frown, I was told that it is only permitted if properly equipped. I pointed to my pony with reg attached to my bc. I also dive with a second computer, depth gauge and watch. The employee, less than happy, grumbled something, walked away. Came back minutes later and wanted to know where my spare mask was. I told her the spare mask was a recommendation and not a requirement. A minute of thought and then I received an unhappy ok and the employee walked away.
Another dive op on CUR who I have solo dived with many times, has a clear no solo diving policy on their website. When I solo dive with them I show them solo cert and confirm I have redundant air and I am on my way. I asked them why if they permit solo diving why they have a no solo diving policy posted. The answer was we just don't want to encourage solo diving.