this is a very solved problem in financial markets: you source quotes from a set list of contributors, ditch a set number of the highs and lows and average rest, possibly weighted in some way, e.g trade volume.
Tom knew full well that it was impossible for a single guy to move the fix - go too high or too low and your submission gets chucked out. In the range, as 1 of 12 others, you aren't going to have a meaningful impact.
The only way of moving it is to get all submitters (or at least lots of them) to submit high or low fixes in your favour. But a cartel like that is never going to work:
1) It means revealing your positions to your trading counterparties and competitirs - not good 2) Others could be the other way round to you, and want to submit fixes against you 3) Even in those heady days of loose standards, setting up and running a cartel would be logistically tricky
So - what to do? Well Tom had a great insight. he realised that athe interbank lending market was pretty illiquid and there was wasn't much mush actual trading to reference. Most banks were submitting "best guesses" and those guesses were based on broker screens like ICAP. The rationale was that ICAP saw all the flows, so ICAP know the levels, so it was reasonalble to base your submission on the ICAP screens (ICAP screens are used as a reference in all sorts of markets, they are the gold standard).
Now Tom also raelised that ICAP weren't seeing much flow either and that their prices weren't much better than guestimates. So - he basically bribed a couple of brokers at ICAP to bump the screens. And that way he'd effectively bump the whole market as everyone was basing their prices on them! (He bribed the ICAP guys by executing "wash" trades, back-to-backs, that have no economic rationale, but generate brokerage fees).
So, in short, yes the top & tailing averaging approach is pretty robust. But of course no system is completely infallible.