She does say that. Then a moment later, says this
So how do you recover something if they were given to you?
How did he find out she became the new broker?
Ok, concede that Hackett (in some instances) can be said to have given the tags to Liara... when remains open and also somewhat within the player's control... depending on the amount of time that lapses after Liara takes over as Shadow Broker and the invite to the ship. How did he find out she became the new broker? Anybody's guess... perhaps she contacted him while "digging" for Shepard's tags and told him? The phrasing is also abiguous enough that Liara could have still found the tags independently and then contacted Hackett in order to officially be granted legal possession of them in order to return them to Shepard (i.e. the Alliance's blessing).
The point is that, at the end of ME1, Liara is a much less experienced person than even when we first meet her on Illium... so much so that either Anderson or Hackett would not probably personally consider it appropriate to send her out looking for a Reaper solution right at the end of ME1. Garrus, at that point is portrayed as being young and impetuous and, possibly (depending on what lines the player selects) going into Spectre training... although we all know that he becomes a vigilante instead. Pressly is dead, Shepard is dead and the rest are a young, inexperienced lot with lots of emotional baggage preventing them from being seriously considered by either Anderson or Hackett at that time for such an important task.
Getting back on topic - all of these sorts of variables are problematic for a reboot scenario since such an endeavor will invariably make at least some player choices "canon" within the reboot (depending on also varying opinions as to what is or is not "keeping with basic tenet(s)" would involve in a reboot). Again, not saying it couldn't be done... just saying it's an issue and that no matter what Bioware does with it, there are going to be parts of the fan base upset with what they do.
IMO, ME:A could already qualify as a "hard reboot" of the franchise, but certainly a lot of other people don't think of it in that way... because we can't even agree on an appropriate parameter for what does and does not constitute a "reboot" which is, by definition: "To start anew with fresh ideas in a way that is consistent with the principals of the original, but not unnecessarily constrained by what has taken place before." (Urban Dictionary)... and the definition is chock full of even more ambiguous terms that people can argue about - e.g. like what parts of the ME Trilogy be considered necessary vs. unnecessary constraints?
Lakus, for example, considers the setting to be a "necessary constraint" and other people, myself included, put it in the "unnecessary" category.