All right, I see your point now.
This isn't something I keep detailed track of as I haven't worked with a CSP/registered agent I wouldn't trust with the records. But, with that caveat: BVI, Samoa, SVG, Panama, Costa Rica, Nevis, Mauritius, Hong Kong, Bahamas, and probably several more.
Just have to look a little deeper than the one sentence summary you might find on some websitessay. In many cases, the law doesn't say︀ specifically that the records must be submitted or held by the registered without any options.︁ In some cases, the wording is "made available to" which could mean all you have︂ to do is provide them upon request. In many other cases, the law empowers the︃ board of directors to pass a resolution saying the records can be kept somewhere else.︄ In Saint Lucia, the law requires that the records be kept where the company does︅ business, which can be a pretty loose definition.
In the case of BVI, for example,︆ let's quote
Harneys (one of the biggest offshore law firms, headquartered in BVI):
IIRC, the list of jurisdictions where it must be kept with the registered agent at all︌ times without exception is quite short. I can think of Seychelles, Belize, Vanuatu, and Anguilla︍ (haven't looked into possible exceptions much). Seychelles and Belize are cheap and disproportionately popular. Maybe︎ that's why it seems like such a big deal.
