You're exactly right.
I took a brief look through the paper. Table 3, glia (rightmost columns) seems to sum up this study nicely. Control group had 817 mice, 3 malignant brain tumors. Highest dose had 409 mice, 3 with malignant brain tumors. Not a significant difference in this entire table at any dose in any sub-population, even at p = 0.05 levels.
Table 2 focused on schwannomas, and they had to dig deep to male mice at highest exposure (n = 207) to get a significantly significant (at p = 0.05) difference. We're talking 3 / 207 male mice with malignant schwannomas at highest exposure. The control males had no cases (n = 412), but we're really in the weeds here where a stochastic variation of +/- 1 mouse makes a huge difference in their tallies. No other significant difference in any other dose in any other sub-population in any other table in this paper.
Kaplan-Meier survival curves (Figure 3 g-h) look just about identical for all doses: we're not seeing a big difference in survival times at any doses. And there's no effort to estimate error bars for those curves. That's a hint about (lack of) replicates.
From what I can see, there was exactly one replicate for each group / arm (e.g., mice exposed to a specific dose). This is not good, because technical and biological variability can cause flukes and false differences. 1 technical replicate per arm: if a technician had a bad day or screwed up a protocol when the exposing the mice to the highest dose, your one measurement set could be off. 1 biological replicate per arm: a weird batch of mice, or a batch of sick mice, etc., could throw off your one measurement set for the arm. Most cell line experiments we've worked with have at least 3 technical and biological replicates, in very controlled culture conditions. You'd be amazed at the variability, even in "identical" cells.
Oh, and read the neat Nature story (summary) where the sex of the scientist performing the experiments on mice can cause statistically significant differences. Because the male and female scents in our clothing can actually induce stress hormone changes in mice. Experiments are sensitive. Replicates are a good thing.