So when she declined the coverage it charged her card $3000 for the full refundable deposit.Well, she hated that more so I called tech support and they said it was either/or.

Buying in declining areas, even if they cash flow, will become toxic if you have to reinvest back into the properties.

Also, if the market declines, the lease option downpayment can hedge my risk.The house is worth about 510k-520k.  

WSJ reported earlier this month that the population of NYC is actually declining for the first time in recent memory. 

Most big name decline renting to students.You need to have parents co-sign. 

Long story short, my my grandfather's heath is on the decline, so my parents are agents over his estate.

(cant knock them for trying) you have the leverage, dont forget that. definitely decline the offer and possibly let them know of a price increase if they get the dog. propose to them that next year rent is going up 3% but if they dont get the dog you will keep their rent the same?

Don't let my response overwhelm you, we live in a state where if you don't list it in your criteria then you cannot decline on that reason. 

Look in your paperwork for a notice regarding the availability of owners title insurance and a signed form whereby you declined coverage.Alternatively you could ask for a policy to be issued now... and pay the premium.

Those markets have been hit with a lot of supply & declining prices as the properties there get killed by exorbitant taxes.