I try not to presume the worst, so let's say he honestly doesn't know (or perhaps suspects, and this is his way of asking for a second opinion).
At least one of those could use a rewrap. Battery wraps (or "jackets" if you prefer the technical term) are ten for a buck, with one dollar shipping, from battwrap.com, and can be applied with a hair dryer. If you have access to two dollars and a hair dryer, there's no reason not to rewrap that battery, unless you'd simply rather replace it. In that case, stick some electrical tape on the ends and bring it in to a Radio Shack or Home Depot (or similar -- anywhere that sells rechargeable-battery devices like cell phones, power tools, etc. is supposed to accept them as well) for proper recycling.