New landlord ordered me to sign lease as is
I'm in san jose, and have been renting my current apartment for over 1 year on a month-to-month. The owner got a new property management company to take over for the previous guy. The new management company has sent us a notice saying we need to sign the new lease or move out in 30 days. After going through the lease, and crossing out bits that seemed a bit questionable (i.e. we are responsible for any broken glass, no matter the cause in big, bold letters, and that we are responsible for furnaces, etc) my roommate received a call from the new landlords saying we have to sign the lease as is or they will send us a notice. I called them back, and they said I could write an addendum and attach it to the lease, but not to cross anything out. That seems a bit shady to me. Should I be worried?
Thanks