You are thinking too much in linear terms with a very old mindset. Keywords and density recommendations in respect to Google and likely Bing as well is absolutely completely wrong. Stop thinking this way.
You do have some problems, however, that has nothing to do with being penalized. You have a performance problem.
Here is where you need to educate your boss. If you fail here, then you have not done your job right. Part of being an IT professional is making your point and moving the environment forward in a more productive way. This can be a learning experience for you and your boss. Please take this opportunity for yourself and your boss. He will be impressed!
The link phrase more information not only has no value, but could be sapping your potential in a very huge and real way.
The first thing you have to remember is that search is no longer linear, meaning that while a web page is still read from top to bottom in the traditional way, and how can it not be, the way the page is processed is no longer following the traditional parser model as much as it once was. The reason for this is simple. Google, has grown up! It has undergone many changes over the years and SEO experts have not kept pace. In fact, by and large, most of them are completely wrong headed and have not paid attention to what Google itself is telling us. Google has two communication channels, one is vague, the other extremely detailed and technical. Following the more detailed route, we can easily see that semantics and the move to a more semantic search engine not only started from the very beginning, but took a huge turn starting in 2007. The details on this is staggering!
Here is what your boss is missing.
Search has rapidly moved toward semantic search. Semantics as a technology is what Google was built upon and has been a vital part of it's success ever since it was a research project. There were several lessons learned early and anywhere that existing technologies could be used to make the results better, it was used. This means that the methodologies that made Google stand out are used repeatedly throughout the entire system. These are not generally new concepts. Some go back to 1975! So what works in 1997, is rubber-stamped and tweaked over time and used in other areas over and over again. This means that while new methodologies are being utilized, the underlying concepts are almost exactly as they were in the beginning. What is new is the scale. Most of the technology drive has been toward scaling the system and implementing lessons learned to other areas.
I have written on the effect of semantics and the value it has on links specifically in another answer recently. I will not rewrite the entire answer, but I will summarize it. I invite you to read the answer for yourself. Keyword phrases and links
You can bet that what was important to Google and Google's success in the beginning is still important to Google today. Why? Because they got it right! There were two very specific things that the original research paper highlighted as being of paramount importance: one, the title tag; and two, the link text and value. Even at this time, Google was taking advantage of semantics to understand the search query, the title tag, and the link text. We are familiar with the original PageRank algorithm where links have a numerical value that is passed from page to page, however, what was not discussed was how the text of a link effects the page the link is on and the page that is the target of the link. Conceptually, Google went against the grain when it announced a fundamental shift in thinking. Previously, search engines felt that the link valued the page the link resided upon. Google said that the link more values the page it links to. It is both really, but Google was right in explaining that the link describes the target page more than it describes the page with the link and therefore the textual value of the link is important to understand because of the heavy importance it has on the target page.
In everything you do, think semantics.
I ask, what value does more information have? Short answer. None! However, *More information on the importance of using widgets and whatnots." does. So does "How our widgets and whatnots are superior.", "How our manufacturing of widgets and whatnots differs from the competition.", and "What the quality difference our widgets and whatnots provides." These describe what the topic is about on the target page precisely.
Please know that it was found that searching against the title tag as well as the link text provides a superior result than searching against the text itself. The results produce higher quality results. However, this cannot happen with links that are nondescript such as more information. This has been known since 1997 and should be one of your primary focal points in your overall SEO strategy.
Again, I invite you to read the answer I linked to. I also invite you to share these answers with your boss. Even bosses with rigid opinions will change their mind when you educate them in a cheerful, enthusiastic, and friendly "I am looking out for you and the company." way. I can tell you from experience there is no greater trust than having a strong boss stand beside you and support you unconditionally because he feels you are a trusted ally in the fight.