If it's a problem so small it doesn't even come to our attention, ownership of ships is utterly irrelevant, because said problem is going to be dealt with very quickly whether by ours or by Imperial Trust's navy.
your missing the point....
I could totally see durin deciding to:
(1): have our allys decide to do things we don't like and us not being able to protest because too much of a fleets power came from them.
(2): roll to have our trade-lines destroyed/looted by pirates but NOT our allys because too many of our ships were gone (either non-existent or off fighting a war). each planet can call for aid from the trust fleet. but that fleet is not at every planet at once, OUR fleet needs to be big enough to stop problems.
mind you, (1) could extend to alot of things, like our allies getting a bad roll with a psyker not being dealt with in time and then decideing to have a rule that has long-last impacts on the trust (and us)
or perhaps our allys who are more conservative end up being more supportive of conservative admech-persons and therefore more able to fly them around on their projects since they would be flying around on conservative-owned ships (increasing their influence as a result) where our ships might force them to act more progressively since they would be under the preview (even if not directly) of a more progressive captain....
hence why I was saying that its the little things that are still big enough that durin might have them influence the quest
let me put it another way, suppose on the next turn all of our more conservative allys lose all of their ships somehow. suddenly they are VERY dependent on us and will have to concide things to us. I forget which planet it was that had a very us vs them mindset and were angry that we were starting to overshadow them.....while its very bad that they had/have that mindset, it IS valid to consider that having more power then your allies means you have more control over what kind of alliance it is and what the alliance does.