To answer this question you must first look into the actions of the Trade Federation as a whole.

Although they were seemingly just a shipping conglomerate that happened to control some of the major trading lanes that stretched from the Core Worlds to the Outer Rim, their actions show that these trading lanes weren't the only thing they used to sway things in their direction.

Since they successfully controlled most of the shipping lanes, they had a large sphere of influence on any planet or group that wanted to change the structure of how things were ran. Before the Clone Wars, this area was rampant with crime, with two of the main groups being the Hutt's and the Syndicate. This fight for power in the criminal underworld led to the creation of a private army by the Federation to protect their interests, but not without large loans from the Intergalactic Banking Clan.

The creation of a private droid army to protect investments was the first sign that the Jedi and the Galactic Republic were failing, so the Federation stepped in and tried to maintain order in the Mid Rim territories. This is where the Blockade of Naboo first comes into archives.

Naboo was openly searching for negotiations with the Trade Federation, as per the request of Queen Amidala herself. When the Federation agreed to hear the talks, Amidala would not agree to meet the Federation in mutual space, so the Federation was forced to come to them. With it's droid army onboard, the Federation was prepared in case the negotiations went south and turned into an armed conflict. The Federation's own senator, Lott Dod, lobbied successfully to the Senate that the Federation had broken no laws while it blockaded Naboo as a response to illegal taxation. After a month-long debate on the subject in the Senate, Naboo's own Senator Palpatine successfully swayed Queen Amidala's opinions and had her wait until the Senate came up with a resolution. Not long after, the local populace on Naboo began to feel the effects from the legal blockade, and an armed conflict took place. Due to this, feelings in the Galactic Senate swayed and the already popular Senator Palpatine was made Supreme Chancellor in the hopes that he could put an end to the conflict. Through amazing deliberations, the blockade ended and the rebellion on Naboo was suppressed.

So to answer your question, the Trade Federation's blockade of Naboo was highly controversial, yet it never broke any law and was therefore legal.

As for the Jedi, no records exist in the archives, so I imagine the supposed role they played is nothing more than an urban legend. The truth of who settled the dispute can be easily seen as one of the first great political acts that Palpatine had overseen. This was just the first action that helped to cement himself as the rightful leader of the now Galactic Empire.

Sources:

Official Imperial Archives located on Coruscant

From Humble Beginnings: the Story of Palpatine by Grand Moff Ardus Kaine

^^^^^Obvious ^^^^^Imperial ^^^^^slant ^^^^^huh?