That is totally and utterly incorrect.
6 Litecoin confirmations are approximately as secure as 6 Bitcoin ones. The amount of time taken has little impact (unless reduced so far that propagation time begins to become a significant percentage of total time between blocks).
If I flip 2 coins then the chance of 2 heads in a row is 25% whether it takes me a second per flip or an hour per flip. It's very similar with finding blocks - the likelihood of any individual miner finding a block is dependent on the percentage of total hashpower they own. Someone with 51% of hashpower will find just over half of all blocks regardless of whether it takes 1 minute or 1 hour on average to find a block. Their chance of successfully starting a 51% attack from any given point will be near enough identical on LTC/BTC - where they have a slight advantage on LTC is that they can make more tries in the same amount of time (but that has nowhere near the impact you indicated).
The fallacy you stated is one widely assumed to be true by those with little grasp of math (or a flawed understanding of how block generation works). It IS, however, a fallacy - lots of semi-numerate people failing at math doesn't make their incorrect answers right.
If you want to understand in detail how you're wrong then Meni Rosenfeld (apologies if I got his name wrong) did a proper analysis of it somewhere.