That explanation is extremely unlikely. Our constraints on the age of the universe are now extremely tight and come from several independent measurements.

What these results are more likely telling us is what the very first generation of stars were like. There's currently a great deal of uncertainty about how they form and what they're like. One of the reasons we know so little about them is because no one has actually seen a first generation star. Such a star would be characterized by having no metals at all. Some stars with extremely low amounts of metals have been discovered (something like one millionth the amount of metals in the Sun), but all have a detectable amount of metals in their atmosphere. This means that: (1) there were very few first generation stars, so they are extremely rare; and/or (2) the first generation stars that formed were extremely massive, so they all had very short lifetimes.

In addition to these observational uncertainties, there are major theoretical uncertainties about the formation of first generation stars as well. Star formation in general is poorly understood, but it is known that metals are extremely important when forming stars. The reason for this somewhat technical, but makes for an interesting diversion. If you have a gas cloud out in interstellar space, it has some temperature. As the cloud collapses under its own gravity, it heats up. However, according to the virial theorem twice as much gravitational energy is lost as goes into heat -- this means that the other half must be radiated away. But radiative transport in these clouds can be inefficient. If your contracting gas cloud produces a photon, it will pretty soon hit a hydrogen atom, bump it up to the next energy level, and then be re-emitted when the hydrogen atom transitions back down to the ground state. This will happen many, many times and the photon will bounce around the cloud for a long, long time before it can random walk out of the cloud, escape, and cool the cloud down. Remember, until the photon leaves the cloud, the cloud cannot contract. However, if this photon hits a metal, electron will jump up to some high energy level, and then cascade down to the ground state through some complicated path and will emit several low energy photons. These photons will be unable to bump any hydrogen atoms up to the next energy level so they can travel through the cloud unimpeded. Thus metals are extremely important for cooling clouds efficiently. The more metals a cloud has, the more easily it can contract and form stars.

A direct consequence of this is that clouds with metals can fragment more easily. This means that a large gas cloud will fragment into many smaller subclouds and form lots of stars in a cluster. In the early universe, however, it's not clear what happened. It may be that without metals clouds just didn't fragment and so the first generation of stars were all truly massive -- maybe hundreds to thousands of solar masses. But this scenario is problematic for a number of reasons -- foremost among them, the gas needs to cool somehow, and the cooling time seems to be too long to form these kinds of stars. There might (probably even must) be some other way to cool these clouds to get them to contract, but what other cooling mechanisms work on clouds without metals is not well understood.

Results like this put constraints on how quickly the first generation of stars must have formed, how massive they must have been (at least some of them), and how many of them there must have been.