When the file was transferred to another desk, they quickly accepted a different offer at 72% (same everything except buyer and price).As mentioned, banks' (investors') assessments of their own liquidity, capital requirements and exposure to the market have a lot to do with it.  

Using an external insurance provider is but way to hedge and manage risk exposure.

They also might say that by leaving all this equity in your property you open yourself up to unnecessary liability and exposure should you get sued. 

I'm getting some exposure to real estate investing through a couple of my colleagues that make a living through rentals and flipping homes.

However in the picture, there is rebar exposure in the bottom of the slab between the supports. 

With a single family home I also have a greater exposure to vacancy as I have a single property with a single renter that I have to keep filled.  

Generally speaking an umbrella policy is rated for 2 key risk factors; assets that you may lose if sued, and exposures that increase your likeliness to be sued.

If you're uncomfortable taking on a lot of risk, buy something smaller, or do it with a partner so your exposure is cut in 1/2. 

As others have mentioned, it sounds like you're not getting the exposure you need. 

When you consider your overall risk exposure (which BTW in real estate should always be as close to zero as possible) with a 1920's duplex it has a lot more to do with the condition of a 100 year old property, than with your downpayment.