observation - Could there be a closer star to Earth than the Alpha Centauri triple star system, excluding the Sun?

In this answer you can find a calculation for how bright "Nemesis" would be at near-infrared wavelengths. This calculation assumed we were looking for a 20 Jupiter mass object with a similar age to the Sun at a distance of 1.4 light years (to fit in with the Nemesis hypothesis). The calculated magnitudes were H=14 and W2=8 (in the WISE infrared satellite system).

If we relax the assumptions and let the object be 4.4 light years away, we have to add 2.5 magnitudes to these numbers. i.e. H=16.5 and W2=10.5. Whilst the former is right on the edge of detectability in the 2MASS survey, the former is comfortably detectable in the WISE survey (limit is about W2=15.6 see http://wise2.ipac.caltech.edu/docs/release/allsky/ ) and the object would have a large parallax/proper motion. Whether this would be detectable might depend on the presence of a good "first epoch" image. In the case of the brown dwarf Luhman 16 at 6.5 light years (but which is maybe 40-50 Jupiter masses), well it showed up easily in first epoch 2MASS images (H=9.6).

Now, your question asks whether a star may have been missed. Such an object would be much brighter than the hypothesised brown dwarf above, or Luhman 16. The "industry-standard" models of Baraffe et al. (1998) suggest that a $0.075 M_{odot}$ minimum mass stellar object at 4.4 light years would have H=7.5. It is hard to imagine how such an object would have been missed, unless it has such a small proper motion that it has not moved significantly between the 2MASS survey in the 90s to the WISE survey in ~2010. This is unlikely (but not impossible).

Once Gaia results are published in 2017, it will have complete parallax data for all stars down to about V=19. This should include even the lowest mass M-dwarf stars out to around 10 parsecs (30 light years).