If I'm interpreting your question correctly, you want to know if it's somehow wrong for an employee to be held accountable for their work/job duties, even if that particular employee has been there for many years.
In a nutshell, no. ALL employees, regardless of age or seniority, needs to be held accountable for their job duties. No matter how long you have been employed somewhere, or how old you are, you are being paid to do a job, and you should do it in the manner that is correct and necessary for others to do their jobs, if applicable.
Long-term employees often get comfortable, which isn't necessarily a bad thing, but when comfort=refusal to learn/adapt, then it becomes a problem.
I think a few responders are viewing your question as an age vs. youth issue, and it's not. It's unfair to say that J. because someone has worked somewhere for 20+ years they should be able to do things however they want, and the newer employees should be grateful to have their jobs and should J. shut up and cover for them.
In your case, it sounds as though this is a numbers/monetary concern, not J. a "I would rather hand write the report than type it" or "I don't read my email, can you J. call and tell M. about it" problem. In this instance, I would document, document, document. If your boss is on board with these concerns, maybe this will be a way for he/she to show how detrimental the lack of adapting/adjusting is to the overall goal of the business, particularly if an audit would result in fines or other sanctions because of the lack of checks and balances.
One more thing....this type of behavior/attitude is not always seen in J. older or the most senior employees. There are many people who have been somewhere for most of their working life but are still relatively young who refuse to do things in a new, more productive or traceable way. I'm not in management or at the executive level, but my mom is, and I often hear from her how difficult people of all ages and employment levels can be when they need to learn a different way of doing things or to change the way an activity is done. Change is hard, but when it comes to your professional life, you need to do it, whether you are 25 or 65, have been employed for 30 days or 30 years.
Age and seniority do not give you a free pass to collect a paycheck without doing the work that your position requires you to do. Perhaps the way you've always done it isn't necessarily wrong, but it's no longer the acceptable practice. Things change, we all need to adjust.