McLaren Racing are seeking some $20 million in a breach of contract lawsuit against the Spaniard over an aborted move to them three years ago.
Palou's lawyers say he owes nothing and have accused McLaren of trying to take him "to the cleaners".
'False promises of F1 glory'
Palou's counsel Nick De Marco, questioning Brown on his witness statement at a High Court hearing, suggested the American had a habit of making "false promises of F1 glory" and encouraging people before "shafting them".
De Marco said Palou signed a contract solely with the intention of getting to Formula 1 and then saw a message on social media from Australian Oscar Piastri saying he was joining the McLaren F1 team alongside Lando Norris, causing him to lose faith.
"All that time you have been stringing Mr Palou along,” said De Marco.
"I never strung along Alex," replied Brown. "I never told him he would be under consideration for 2023 ... there was some optionality to join F1."
Brown said in his witness statement that he believed Palou could be "a real talent" in Formula 1 but he had always managed his expectations.
He said Piastri, now the championship leader in a battle with Norris, was signed on a one-year contract and Palou was the "Plan B" if either of the race drivers were injured. Plan C was for Palou to replace Piastri in 2024 should the rookie fail to perform.
He cited the examples of Oliver Bearman and Nyck de Vries who landed full-time drives after stepping in as reserves at Ferrari and Williams respectively.
Palou ultimately stayed with Chip Ganassi Racing and won three consecutive IndyCar titles from 2023 to 2025, after his 2021 title, plus the Indianapolis 500.
De Marco accused Brown, who celebrated his team's second successive constructors' title in Sunday's Singapore Grand Prix and then flew back to attend the court hearing on Monday, of being evasive and dishonest in much of his evidence.
Brown, who strongly asserted his integrity, had been asked about the deletion of WhatsApp messages and dealings with other drivers, including Mexican Pato O'Ward who races for Arrow McLaren.
In one testy exchange, the lawyer said Brown was speaking "absolute rubbish, made up on the spot" - to which the American replied that De Marco was the one talking rubbish.
Brown is due to face further questions on Wednesday before Palou has his turn in the witness box on Thursday.