I am wondering if thats just sales patter for a mutually agreed reduction in the deposit amount between buyer and vendor?
It cannot just be an agreement between buyer and vendor the lender/surveyor have to agree to the lending too.
In general you can't get a mortgage of £162K for a £170K value because that's higher than a 95% LTV which is risky for the lender.
So the mortgage lenders surveyor has to agree that the property is actually worth £180K so it's a 90% Loan to Value.

Its potentially legit although genuine "below market value" properties are usually snapped up by estate agents and their circle of friends.

If you were an estate agent and came across something genuinely 10K cheaper, you'd tell your friends, family and mates wouldn't you.
Perhaps this is a genuine tip off situation and if it's affordable there is no issue, but alarm bells ring if people claim to have no spare cash. Owning costs money beyond the immediate mortgage and you don't need to be an IFA to know about the practicalities of monthly household budgetting.