That's fine. For the vast majority of people it's a terrible way to invest your money and whether or not Burren is doing it, other people are aggressively marketing it to people who barely have anything to invest and they are getting sold on "infinite banking" horseshit that is being advertised as a smart and sound investment when it will mean orders of magnitude less money when you retire if you fall for it and keep doing it for a long time. My grandfather bought a couple of them and I have received these sales pitches myself and you would think they are giving you the keys to a happy life when all they're doing is ruining your retirement for their own gain. I'll take your word for it that there are rich people fucking around with it to avoid taxes etc, but 95% of people should run away from that shit and any national radio program would be irresponsible to say anything else.
EDIT: BTW, annuities pay very high commissions for obvious reasons so financial advisors have a lot of incentive to rationalize why people should buy them. Conversely, they can't make much money at all by telling people to invest in index funds or simple mutual funds.