Joyce's Twitter exchange was more prosaic than the US President's, but no less focused.
What got up Joyce's nose was the implication that Pellett - who is a cherished Labour Party favourite - was having a bob each way on the issue du jour: whether Endace should pay back $11 million of Government R&D loans it received before it passes into 100 per cent foreign ownership, substantially enriching its founders.
Let's say upfront that Pellett has been a thorn in the Government's side.
He is a spokesman for the Productive Economy Council and has kicked the Government's shins hard over its plans to sell down its holdings in state-owned assets. So it's no surprise that Joyce - who has been remarkably unrestrained recently - took the opportunity to have a slash back.
What annoys Joyce is the fact that as a former Endace boss, Pellett used to have significant skin in the game. Not as much as founder Ian Graham, who told me he would be spending more time on his boat after he sells his holding to the new American owners, but enough to raise the hypocrisy red flag with Joyce.
The Twitter battle between Joyce and Pellett was great sport:
"So you collect taxpayer support, decide to sell shares, make lots of money & then moan about it in @nzherald #unbelievable ... BTW R & D co-funding is about doing R&D in NZ, not supporting individuals. But happy 4 u 2 repay so we can fund others," Joyce tweeted at Pellett.
Pellett tweeted back: "Mr Joyce, you should check all yr facts. Interesting a Minister would target an individual for speaking out on policy."
In a subsequent tweet, Pellett said: "@stevenljoyce on record 4 a long time about the need to get grants stopped & switched to convertible notes. Public agree why not?"
Joyce knows Pellett has a point.
Many of our entrepreneurs who have sold their companies offshore have done very well indeed through a helping hand from the Government. Huge sums of Government cash are "invested" in NZ firms but without the kind of strings a private sector investor would insist on for their "investment". That's because the so-called investment is wrapped up in a rather woolly public good concept when most of the upside is basically privatised.
The Government does not take shares in the enterprises which it "invests" in. The argument goes that this could expose the Government to being asked to stump up for more funds if the company ran into difficulties or wanted more cash to expand..
When high-tech companies are sold offshore - as so many are - the funding agreements have sufficient wriggle room that the owners do not have to pay the Government back out of their profit. The Government is simply persuaded (as with Endace) that it is better to leave the funds "invested" to stop the new owners moving R&D and/or jobs offshore.
Fundamentally this is a copout.
Pellett has suggested the Government take "convertible notes" in enterprises so that it can get the cash out when ownership changes hands and "reinvest" it to another company on the way up.
This makes sense.
Corporate welfare largess is much bigger than is commonly known. Sir Peter Jackson gets it in the neck over the extent of taxpayer "subsidies" the film industry receives to attract big motion pictures to New Zealand. As the New York Times reported this week, Hollywood may make films about the evils of capitalism but it rarely works without incentives, which are paid for by taxpayers.
"Nationwide, about $1.5 billion in tax breaks is awarded to the film industry each year, according to a state-by-state survey by the New York Times," it said.)
In New Zealand, the public primary partnership fund is providing $600 million of Government funds to co-invest in agriculture firms to develop new products.
Just last week, the Ministry of Primary Industries announced Anzco Foods - a private company controlled by Sir Graeme Harrison - would receive $43.5 million over six years to develop new products from beef carcasses.
Anzco Foods will match the Government "investment".
But in these tight fiscal times, it's worth asking if the taxpayer should get something more tangible than a public good for his or her investment.
Joyce and Pellett would do us all a favour if they continued their Twitter battle.