No. It is good you brought this question because it will educate many of us. This rule against dependence of clubs was adopted around 1998 and towards 2001 it became active. It prevents clubs that are directly owned and financed from one source to participate in UEFA competition.
I think the major reason for such role is to avoid match fixing. Imagine where the one of the two clubs is yet to qualify and they are to play each other, so what will happen in such instance, of course match fixing.
This is why I love football. It is because amidst the fact that humans cannot run away from errors that are as a result of interests, they still try as much as possible to look critically and legislate rules that will ensure that there is sanity in the game and a sense of fair play in the system as an entirety.
This rule on clubs owned by same entities not allowed to participate in champions league was a well-thought out idea and this is because although the both teams will be run by different management and may have different orientations as well as they may be very competitive to one another, that is not the only issue. Another issue is that both teams can be easily bias when they are fixtured in the same pitch.
For instance, one club can decide to make it easier for the other club to win because the owner must have arranged the plan to the advantage of the latter club and reasons to that can be due to when one of the club is seen as more promising to the other, that bias can come in immediately to favour one another.
Another instance is when they play same table, they can plan on ways to sabotage other clubs and even when that may seem incredibly difficult to do, they can still bring about that insecurity and fear in the minds of the other teams.