Is this landlord a scam?

I found a random person with no LinkedIn or regular Facebook profile asking around in a Facebook sublease group, reaching out to 3-4 people about interest in taking over a lease. I contacted a girl who was polite and explained that she wanted to move out and transfer her lease to someone new. The lease is for a room in a good location (College Terrace), just near Stanford University, for $1,300, including utilities.

I got excited and asked how I could take over the lease. She requested my email, saying that the landlord would contact me. About half a day later, I received an email from the landlord asking for basic information—nothing sensitive—such as whether I own pets or a vehicle, my income, how long I plan to stay, and a bank statement. In my bank statement, I only disclosed my balance over the month and nothing else. The form was a full PDF that I had to fill out.

A day later, I received a reply saying I was approved and that the landlord wanted me to sign the PDF and send $2,300—$1,300 for the first month’s rent and $1,000 as a security deposit. The issue is that I’m not currently in Palo Alto, so I don’t know how to verify if this is legitimate. I tried contacting the girl who advertised the lease, but she’s no longer responding.

Does this sound like a scam? Also, how cheap is this for a unit in College Terrace?