The actual research doesn't claim that more/less innovative projects are more/less funded. The use of 2SLS/instrumental variables explicitly rules out unobserved variables (including how innovative the project really is). Hence, the research only makes claims regarding the extent of novelty and usefulness claims and does not speculate on the underlying nature of the project.
The evidence does not support exaggeration. Making novel and useful claims is linked (causally) to much more money being pledged to the project. In fact the effect size is staggering. With exaggeration, the community should discount the project description. But it doesn't.
What is surprising is that if people fund more if you say its novel, and they fund more if you say its useful, why do they fund less if you say its both novel and useful? Why do they respond positively to novel, and positively to useful, and negatively to the joint of these. This effect is stable across categories, across time. It does not seem to be a learning story (backers learn that novel + useful is more risky and hence better not funded). It seems to be something more fundamental about how we as consumers/individuals respond to innovation claims. But the evidence cannot rule out all confounds: the work is more exploratory than confirmatory.
Re: measuring innovation. Arguably this is a more important question. But the extent of innovation depends on a potential backer's knowledge and their own needs. What is new to someone, is not new to another. What is useful to someone, is not new useful to another. This is an active area of research so other methods may help address this issue. But it would be cost prohibitive to do this at scale using archival data.
