Considering how easily she ended up giving in, it clearly wasn't much of a stretch for her to use her power on it.
The concerns over setting a precedent is Rin's job (and she did bring up those concerns), not Christina's, since the effect of that would be within the company. And Christina is not actually part of their company. Once Rin ordered them to stop their other work and dedicate their work hours to the prototype, it stopped being an unauthorized project, so those concerns aren't really relevant to the presentation itself.
The presented schedule was also drawn up by Rin, who successfully managed the schedule for PECO. If she thinks the schedule is workable, I'm not sure there's a reason to distrust her on it.
And as Hazuki kind of pointed out in the bonus page, someone took a chance on her when she was unknown in order for her to get where she is now.
Christina, an outside party, was also basically telling Eagle Jump that sorry, we don't care what project your company wants to push; we're not going to let you work on anything Hazuki didn't make.