No, the idea of ALF's investment methodology is that its returns are to a great extent independent of market movements. Essentially they buy stocks that they see as undervalued, but then they also offset this by shorting (essentially selling) a similar level of stocks that they see as being undervalued. If they offset within the same industries eg buy one mining stock and short another mining stock then if the mining industry plummets, in theory (if they pick the right long & shorts) they won't suffer as badly (or at all) because they are both long and short (essentially hedged). It can conversely mean though that when the markets are going gangbusters, the shorts can drag on their performance. It really relies on them getting their longs and shorts right, if they do they can seriously outperform (especially during market downturns) but if they don't then their losses can be magnified. I sold out (luckily still at a small profit) a while ago after a period of underperformance, thinking that their investment style just wasn't for me.
I think he was talking about managed funds rather than LIC's per se, and their underperformance was in a big way due to the fees that they charged. There are several big LICs that charge no fees, and whose management expense ratios are as low as 0.13%.