at arm's length -> independent

The arm's length principle (ALP) is the condition or the fact that the parties to a transaction are independent and on an equal footing. Such a transaction is known as an "arm's-length transaction". It is used specifically in contract law to arrange an equitable agreement that will stand up to legal scrutiny, even though the parties may have shared interests (e.g., employer-employee) or are too closely related to be seen as completely independent (e.g., the parties have familial ties).
http://en.wikipedia.org/wiki/Arm's_length_principle

Arm's Length Relationship
An arm's length relationship is a term used to describe a type of business relationship a corporation should have with a close associate to avoid a conflict of interest. For example, when you negotiate with your banker or your supplier, any agreement which results will likely reflect market value and commercially reasonable terms and conditions.
http://apostille.us/abc/arms_length_relationship.shtml

arm's length adj. the description of an agreement made by two parties freely and independently of each other, and without some special relationship, such as being a relative, having another deal on the side or one party having complete control of the other. It becomes important to determine if an agreement was freely entered into to show that the price, requirements, and other conditions were fair and real. Example: if a man sells property to his son the value set may not be the true value since it may not have been an "arm's length" transaction.
http://legal-dictionary.thefreedictionary.com/arm's length

The parties are admitting that they may be acting in their own interests and on special terms - as they are perfectly entitled to do.

However, most people wishing to do business with them must trade on normal market terms, and these still have to be assessed or negotiated.

Specially favourable terms can be agreed between family and friends, depending on what the business is, and the law of the country.

For instance, in Denmark, the owner of a house may sell it to certain close family members for a sum 15% below the market price, but any greater reduction will attract tax one way or another.

Other rules apply to other kinds of business.

Others can probably explain better!