There's truth in those rumours unfortunately. I know of at least one development studio that only received their kit about 3 months ago, which has impacted on the development of their project. I'm not going into names and details as it isn't my place to do so and I don't want to jeopardise any potential future work! LOL!
I'm reluctant to say too much more as the effort from Microsoft, AMD and developers (and Sony with their PS5) has been commendable. It's easy to criticise but knowing what has gone into making the launches of these consoles possible (and actually having some titles to play, even if not yet taking advantage of all the new hardware) I think the future looks good for console gamers.
Most existing games [early-on] will simply be relying on a few simple tweaks and updates to improve their looks and performance on the new console. In fact, many will just rely on the increase in raw performance of the CPU and GPU. The main issue, as is often the case, is one of time and resources - which are often limited in this line of business. It is not necessarily trivial to go back into the codebase of an existing game and to enable these new features. Depending on the way the game is architected it may need a ground-up refactor. It's not simply a case of flicking a switch to enable a feature unfortunately. Are publishers (and those that fund the developers) willing to spend significant money on revisiting existing titles in an effort to shoehorn in the new features? Likely not in most cases as new projects will already be underway and that's where the money will be spent. Personally I would love to see some of my favourite existing games overhauled to take advantage of the new tech, but I can't see it happening. There's a big difference between replacing a game's assets with a higher resolution 4K texture pack and rewriting that game to overhaul the engine to take advantage of an improved rendering pipeline and faster content delivery architectures.
With APIs now in a much more feature-complete state we will no doubt start to see these new features leveraged in upcoming titles. It's hard to say to what level and when, though - writing a game is such a complex thing to do. With games costing millions to make these days, involving teams of hundreds of people in some cases, and having been in development for potentially a number of years already, you can't always just drop what you have to factor in new 'stuff'. There's obviously a risk to doing that. We - as gamers - need to exercise a little patience sometimes. Again, I'm not going into detail but suffice to say that a good number of development studios are only now seeing finalised APIs and have only recently got their hands on actual working kit. No matter how talented said development studios may be, they will need time to familiarise, understand, digest and experiment with what's available - and then figure out how to best use it in their games (whether that does involve revisiting older games to overhaul them or, more likely, in the development of forthcoming games).