This question arises most frequently in corporate counsel situations. The attorney-client privilege is recognized to apply to communications between corporate officers and corporate counsel where the subject involves matters traditionally performed only by an attorney.
For instance, discussions with the corporate attorney involving pending or threatened litigation are protected by the privilege. On the other hand, if a board of directors has an attorney as a member, materials related to board discussions are not thereby priveleged. (sound practice dictates that attorneys on a board of directors not render legal advice to the corporation and attorneys who render legal advice not serve on the board of directors)
Although avarice drives well-connected lawyers to it, lobbying is recognized as not constituting the practice of law. It's not illegal for attorneys to do it, but they're not acting as lawyers when they do.
Your analysis is the correct one, although as a lawyer I kinda wish you could have used a little more upscale example for comparison.
At least he didn't use the operator of a honey wagon as his example.