The target audience of their covered call strategy is:
"For stock investors seeking a relatively low-risk alternative yielding a return superior to that of most bonds, Berkshire Hathaway covered call options are an attractive proposition. While stock options are used by some investors to speculate, others use options to reduce risk or earn income. This strategy is part of the latter group."

So, apparently the audience are those that don't like bond funds e.g. due to interest rate risk, and uncomfortable with general equities, but like BRK. They show some results for their covered call strategy on BRK. Their numbers are net of their fee, so it'd be better DIY. They don't specify how they're selling their calls, i.e. how far OTM, lifetime, hold time, if they sell all the time regardless of volatility, etc.

Put/call parity aside, are their returns better than "most bonds" as per their stated goal? Yes. Is that the only criterion you should care about? Presumably not, among other things their vol looks higher than their bond benchmark, and while they show a graph they don't give drawdown stats.

Regarding their 'private program' that "employs one and two year stock opions" on BRK, they again don't give details. I think I assumed DITM calls just because that's top of my head. But from their strategy yearly numbers it doesn't look like they are (solely) buying long-term DITM calls.

The Check site used to show Value Line style reports on their holdings, which is why I noodled on over. I didn't find those this time, but instead found their stats on two option strategies that they employ on BRK. Strategy details are lacking, but I was surprised to find real world stats on some options strategies on BRK employed by a large well-established firm. There are lots of ways to skin that cat, chacun à son goût.