I keep going back to the early days of the game to see if there is anything there that makes it clearer (no, if you are wondering). I note the following for your amusement.
The first time you get a chance to check your email is in the evening of the first day. The walkthrough doesn't even suggest that you check it. Why, because there is nothing on the phone. And yet you and Monica have connected through the mysterious email that she got that you didn't send.
The next time you get a chance to check emails, it's the morning of the next day, I believe. And there are emails from friends saying that they don't have the space to have you come live there. So Monica is at least a day quicker to respond than anyone else, and everyone (I should capitalize that) else responds within a 12 hour period.
Now, it's possible, even probable that everything there is on the up and up, but (put your tinfoil hats on now guys) what if someone (Elaine or Bella) having access to the MCs phone sent one and only one email to Monica. Then, after Jenna hears that MC didn't send the email, and she, being the hacker she is, hacks MCs phone with fake incoming messages from some of his contacts saying that there is no room at their place.
This sort of ensures that the MC will stay connected to Monica and the girls which is a plus for Jenna.
This is, of course, not completely thought out and probably a non-starter in terms of what really happened, so feel free to hack it to pieces. It won't upset me in the least.