I think you've hit the nail on the head.
The naquadria is of vital national importance.
At the end of the episode, the SGC had no formal diplomatic ties with the Kelownans.
The main reason that they're so keen to jump straight into friendly relations with the Kelownans is so that they can get their hands on this potentially war-winning element:
HAMMOND : Give me some credit, Jack. I will tell them that we did not order any such action and do not condone its obvious intentions,
both of which are true. Hopefully, we can lay the groundwork for
further diplomatic negotiations which will eventually result in an
amicable trade for the naquadria. I'm ordering you to deliver the
When Jonas arrives claiming asylum, it basically scuppers these negotiations. With no (formal) diplomatic ties with the planet, they're left under no moral or legal obligation to return the things that Jonas brought with him.
Jack O'Neill puts this very nicely in Shades of Grey
O'NEILL : Our core mission is to go through that gate and find technologies we can use to defend against Goa'uld incursion. Am I
HAMMOND : You are bordering on insubordination. We do not steal from friendlies.
Kelowna, at this point isn't an "unfriendly" but they certainly haven't acted honourably either.
Later, in Homecoming, we learn that since Jonas' defection the Kelownans have made some attempts to normalise relations with the SGC but only for the purposes of defence. This was refused and would presumably include handing over weaponisable naquadria, even if it was theirs in the first place.
DREYLOCK (over the radio): This is Ambassador Dreylock of the Kelownan High Council. Please respond.
HAMMOND: This is General Hammond of Stargate Command.
DREYLOCK: We request immediate assistance. We are under attack.
HAMMOND: We've been over this, Ambassador. We can't interfere in the internal affairs of your planet.
On top of all that, the SGC are smarting from the loss of Daniel Jackson. You could certainly argue that having saved the lives of millions of Kelownans, they're entitled to conduct scientific studies into the element that caused his death.