I wonder if it's because Liam's used to anyone he deems "regular (ordinary)" simply cowering before him, that Hoshino facing him down--despite her physical temerity--is what's got him spooked.
If she were truly a fraud, perhaps he figures she'd crack under the pressure of being made to "walk the talk". That she isn't, while being up-front about stuff like the fact she won't breach confidentiality--even if it'd "mean her loss" in their little game--probably is setting off alarm bells for Liam, because she's reacting entirely counter to his lived experience (at least insofar as what we've seen in the chapters he's appeared in, when dealing with anyone who wasn't Elnston or Sage).
Which, given how he seems relatively straightforward as an individual, is raising his hackles. Someone who appears weak and mild, not being that way in a manner that reads as authentic, is enough of a discordance that it'd make any individual accustomed to clear definitions of "power" second-guess their situation, I wager.
Unsure of how this'll proceed, except that I assume Hoshino will ultimately "win" and convince Liam of her ability and her utility for the Hero's Party. How that happens, and what transpires past that - well, I look forward to seeing it all play out.
Thanks for the chapters.