Nah.
Let's say for arguments sake that the money in 2007 was indeed legally a gift to Moshiri, which is in itself massively debatable, then it still Moshiri's asset to do what he likes with. If Usmanov had winged funds around to evade tax or something then rebought to offset his tax bill, then sure it could be investigated. But it was nearly a decade later that Moshiri sold up and he did so to pursue a clear other interest - the shares in Arsenal at that point where indisputably his property.
As the last sentence says, the Premier League know full well his purchase was legit - this reeks of Panorama starting an investigation, finding nothing but wanting to use the work they've done to make a program so it doesn't go to waste. They'll target Usmanov and front load on the 'evil billionaire foreigner' angle without providing proofs of anything; just insinuation.
For what it's worth, I still have no doubts at all that Usmanov will be here eventually. But it'll be done legally, albeit sneakily.