The 1996 Atlanta Olympics in the US were late July to early August. So there's no excuse for that reported scheduling of the 2028 summer Olympics.
As such the Tour should just ignore it & carry on as per usual. It'll always be way bigger than the Olympics anyway (for cycling that is).
That year the Tour ended the same weekend as the Olympics began. If they follow the same pattern, it will start at June 23rd.
The thing is also media attention. The Tour is now a much mediatic product than it was 30 years ago. It's a multi million dollar product and can't afford to share media time and resources with other global sports products. Does ASO want to have their race decided while the world's attention is focused on some other product? Media outlets may need to divert resources to the USA, etc. And while in France the Tour may keep the biggest share of the audience, I don't think the same applies to other markets (particularly outside Europe) that ASO may have their eyes on.
In 1996 it was also the first time cycling was open to professionals, nowadays is also a much more valuable goal for cyclists.