This is a fairly nasty difference from the standard GPLv3 that I don't think enough people appreciate. As you point out, companies that modify GPL code for internal use don't have to release the source code and aren't affected by most of its provisions, and this is intentionally one of the freedoms it gives users. This isn't true of the AGPLv3.
DannyBee said the word "access", and technically that would then be "read only" access. While I could conceive a situation in which a disgruntled contractor plus the original author could in theory make a case, read-only access is a odd thing to create a court case around and a judge decision could really go anywhere. I don't think anyone would be willing to test it or feel that the court costs would be worth paying for the privilege.
Seems rather clear cut to me how contractors are handled. Since we are talking about legal risk and risk is measured in likeliness of an event happening, and as a lawyer you were expected during training to find and provide legal precedence as proof for legal reasoning, how high risk is there that this would not cover internal systems, temps, vendors, and contractors who access those systems? Has there been any cases involving that kind of employee status, having access to source code with similar licensed agreement, and the court finding a decision which support your conclusion? If you worked for a insurance company, how much money per month would you advice them to charge for this "risk", and would you then in good-faith advice companies that it is a good deal rather than shouldering the risk themselves?