The official novelisation offers a very slightly different version of events as well as some more information about Qui-Gon's reticence to help. In short, because her plan involves recruiting the Gungans to fight in a war against the Trade Federation, the Jedi can't give the impression of being on one side or another:
Obi-Wan understood. Who could say? Perhaps this time Qui-Gon was
right. Perhaps Anakin Skywalker’s training was a cause worth fighting
“I’ve been thinking,” Qui-Gon announced suddenly, keeping his voice
low, his eyes directed toward the others. “We are treading on
dangerous ground. If the Queen intends to fight a war, we cannot
become involved. Not even in her efforts to persuade the Gungans to
join with the Naboo against the Federation, if that is what she
intends by coming here. The Jedi have no authority to take sides.”
“But we do have authority to protect the Queen,” Obi-Wan pointed out.
Qui-Gon’s eyes shifted to find his. “It is a fine line we walk, then.”
There is of course the option of using their Jedi mind control techniques to influence Boss Nass' decision in the favour of the Queen.
The Jedi Path Manual describes the ability to affect the minds of others (mind control) as one of the most dangerous of Jedi abilities and one that should only be used sparingly and to accomplish the "greater good". Tricking a largely peaceful people into fighting a war certainly doesn't meet that criteria:
Affect mind, commonly referred to as the "Jedi mind trick," can override the impulses of an undisciplined brain. This ability should
be a temporary means to accomplish a greater good. It should never be
used for profit or gain.