Ryujin
Legend
Most of that dense starfield is just that - a starfield, not a collection of known objects. Something less than 1% of the stars in that dense starfield have been cataloged.
Now, note that I also spoke about occultation of "bright" stars. That's because there are actually lots of stars in the catalog. Too many. Like, a bit short of 950 million in the Guide Star Catalog. There is no way you're going to watch to see which of 950 million stars got occulted. It doesn't matter how impressive your computer power is. The fact of the matter is that we are not *constantly watching* 950 million objects. We are not taking nightly catalogs of the entire sky that resolves each star. We have not even taken nightly catalogs of the regions we suspect the planet is in, because we had no reason to. The data you'd want simply has not been collected.
Specifically bright stars, however, get a bit more attention, but there are far fewer of them, and that leads to the problem that in all likelihood, none of those *just happen* to be in the path.
In addition, as I've been writing I've been realizing - we are talking about a thing that has an orbital period of 10,000 to 20,000 years. That means, since the time of Galileo, it has gone across an arc of *at most* 14 degrees of sky - a smidge less than the distance across the sky the Sun or Moon moves in an hour. In the time that we've had really serious telescopes and major catalogs such that we might have seen the occultation, it has gone more like 1 degree of sky - the distance the Sun or Moon moves in about 4 minutes (plus a little bit for parallax).
So, not a lot of opportunity for occultation.
Not having data on the stars in question would certainly be an issue. Not 'constantly watching' 950 million objects does not preclude them being in arcs that are being actively viewed. True, the swept arc caused by our movement with respect to a proposed object might not get anywhere near something we'd see in our lifetimes, or many multiples thereof.