Buying a house below market value (not a family member) Problems and Benefits?

I don't think this should put your mind at ease either way. Both the vendor and yourself have a potential tax liability for different reasons and him being relaxed doesn't necessarily mean you should be.

I agree with @T McGibney on this - you should seek specialist advice from a tax adviser and/or solicitor.
 
You kind of need to establish if it is truly "below market" or they are just agreeing a lower priced sale than they could push for on the open market.
And if that still is the case, the difference *might* be considered as a gift.
 
From a legal and tax perspective "stranger" just means someone you are not related to.