I do argue that none of the wavelengths seen are due to CNO fusion and assert that there is significant evidence in favor of this position. The bumps in figure 5a are superimposed on top of a sloping background that resembles figure 5b. That background is a thermal continuum. The bumps indicate "background + process", where the neutron capture gamma rays (they are the "process" part) are emitted in addition to the background gamma rays. If there is any CNO fusion process in play then there must be a bump for that process. Furthermore, the CNO process is a cycle, so you don't just get a bump here or a bump there, you get all of the bumps simultaneously or you get none of the bumps at all, there is no middle ground.
Figure 5a covers the energy range 0.3 - 8.0 MeV. So for the CNO-I cycle we should see bumps at 1.95, 2.22, 2.75, 4.96, 7.35 and 7.54 MeV (not "or", but "and"), For the CNO-II cycle we should see bumps at 0.6, 1.19, 2.75, 2.76 and 7.35 MeV (the 12.13 MeV bump lies outside the plot range). The plot shows bumps at about 0.9, 1.5, 2.3, 3.0, 4.6 and 6.0 MeV (the latter being almost invisible and the 1.5 MeV bump being very broad). There are also significant dips at about 0.7, 2-3, 4.5-5.0 and 6-8 MeV. The ~2.3 MeV bump, labeled "n", coincides with 2.23 MeV neutron capture on a proton, and also with the 2.22 MeV gamma ray expected from the inverse beta decay (positron emission) of 13N to 13C in CNO-I . However, the locations on the plot where one would expect to find CNO-I gamma rays at 1.95 & 2.75 MeV are actually dominated by dips in the spectrum, indicating a deficit of gamma rays in the data, where CNO-I would present a surplus of gamma rays. The bump labeled "C" could mask a 4.96 MeV CNO-I bump, but again, there are actually dips rather then bumps, where we would expect to find CNO-I gamma rays at 7.35 & 7.54 MeV. This is not simply an absence of positive evidence that the CNO-I cycle is in play. The presence of dips where there should be bumps constitutes positive evidence in favor of the assertive proposition that the CNO-I cycle in fact is not in play in these data. Likewise, the last 3 bumps one would expect from the CNO-II cycle sit where the data plotted in figure 5a show negative features, while there is no sign of any bumps at 1.19 or 0.6 MeV. And once again, the presence of dips instead of bumps is equally positive evidence for the assertive proposition that the CNO-II cycle is not physically present for the time & place represented by these data.
And so I stand by my claim: These data do not indicate the presence of any CNO fusion cycle. Furthermore, these data do indicate that no CNO fusion cycle is in effect.