Told on one occasion that he should be concerned about the potential impact of a policy initiative on the Italian currency, he memorably replied, "I don't give a f*** about the lira", which was honest, if a little short of being diplomatic.
On another occasion, he stepped up to introduce the man he had nominated as chairman of the Federal Reserve, the economist Arthur Burns. "I respect his independence," he told the assembled company at the White House ceremony. "However, I hope that independently he will conclude that my views are the ones that should be followed." When this was greeted with a round of applause, he smiled and turned to the new Fed chairman: "You see, Dr Burns, that is a standing vote for lower interest rates and more money."
On that occasion, most contemporary historians agree, the central banker may have taken the implied advice of the President, an old friend of his, rather too seriously. The lax policies which Burns presided over contributed to the economic recovery which helped to get Nixon re- elected in 1972, but they proved something of a disaster thereafter, as the US economy slid into inflation and towards the great economic crisis of the mid-1970s.
Even before Opec ratcheted up the price of oil, there was simply too much easy money around and prices generally moved out of control. Arthur Burns left office with a much lower reputation than he enjoyed when he first took over.
We have been luckier with his successors, but it has still taken 20 years for all western countries to come to the conclusion that a genuinely independent central bank is a necessary bulwark against the insidious incursion of inflation.
When the new Labour Government, as one of its first acts last year, handed control over interest rates to an independent monetary policy committee at the Bank of England, it was a welcome sign that this new orthodoxy had spread a long way across the political spectrum.
Investors in particular have paid a high price for allowing governments to manipulate interest rates in the past. Politicians are always likely to find themselves, like Nixon, erring on the side of easy money, in the knowledge that the bill for lax monetary control need not come in until at least two years later - which often (strange coincidence) happens to be after the next election.
The markets were right to take a positive view of the decision to hand control of interest rates to the Bank of England. The decision has clearly been a factor in the continued strength of the market over the past 15 months and the continued decline in inflationary expectations over the same period. But the mistake that many investors make, as we have again seen this week, is to believe that the act of making the central bank independent is in itself a solution to the problem of inflation and erratic growth. It is not - and for a simple reason.
That reason is that determining the right interest rate policy is extremely difficult. Quite apart from the fact that interest rates are a very blunt instrument, which affect different groups of society in different ways, it is also perfectly possible for highly learned and reasonable experts to study the evidence and come to completely different conclusions, not just about what to do, but even about what is happening to the economy in the first place.
Economies are complex social systems, and judging where we are at any stage in the cycle with any degree of precision is effectively - and unfortunately - unknowable. That is one reason why economists' forecasts - just like weather forecasts - tend on balance to be wrong so often: there simply is no clear-cut answer, except, of course, in hindsight.
What matters most is not who is making the interest rate decisions, but whether or not he/she (or they, if it is a committee) are able to come up with the right answers. To put together a track record as a successful policymaker in this area, you need luck and judgement, as well as economic expertise.
Alan Greenspan, the current chairman of the Federal Reserve, the US central bank, has enjoyed a quite extraordinary record of success in the past few years. The US economy has never before enjoyed such a long run of continuous growth allied to low to non-existent inflation. There are times, it is clear, when even Mr Greenspan wonders how it has all been achieved, since he knows that while the press likes to portray him as omniscient, the reality is very different. He has much trouble at calling the runes as most of the rest of us do.
In the UK, the new monetary policy committee which now sets interest rates in this country seems to be having a similar difficulty. This week it put up interest rates again by 0.25 per cent, despite the fact that only a few weeks ago it seemed to have come to the conclusion that interest rates had risen far enough to choke off any serious risk of inflation exceeding its 2.5 per cent target.
The minutes of last month's meeting (also published this week) reveal that at the time, while the majority of the committee's seven members favoured a cautious wait-and-see policy, one of its members wanted an interest rate rise and another believed an interest rate cut was more appropriate.
Both the dissenters were, you won't be surprised to hear, economists - and we know they cannot agree on anything. Even so, while many professionals in the market say they are puzzled by the latest interest rate rise (which most had not expected), my view is that it may actually be a good thing that the committee is so divided in its opinion. (Anyone, incidentally, who wants to can now read the minutes on the Internet and judge for themselves where the argument lies. The web site address is http://www.bankofengland.co.uk.)
The important thing to note is that so far the committee seems to be doing its job reasonably well. While short-term interest rates (the ones set by the Bank of England) are rising, long-term interest rates remain at their lowest levels for many years. Inflation expectations (as implied by the price of gilts) are also still on a downward trend. This remains a favourable backcloth for investors. The time to start worrying in earnest is when the situation reverses.
Easy money today and rising long-term interest rates are what Arthur Burns delivered all those years ago in response to Richard Nixon's plea. Not a happy combination - but one which still today seems remote.