I'm sure there are many clients who have little idea of the level of expertise required to complete their job. I can tell what level of expertise is actually required by reading the job description and getting more details during the interview; I don't much rely on the client's opinion unless the job post indicates that the client is quite knowledgeable about my specialty.
I usually interpret the expertise level specified in the job post as a rough estimate of the amount of money the client is willing to pay. So if the job is labeled "intermediate" but actually seems to require expert-level skills, I may consider not bidding at all because the client likely doesn't understand what's needed and may be hesitant to pay what I ask. Sometimes I bid (my regular rate) and tactfully explain in my proposal that the job is more complicated than the client seems to understand.
If the job is genuinely below my skill level and I really want the job, I might bid lower than I'd normally bid, but you might want to consider what lower rates in your Work History communicates to future potential clients.
Under no circumstances do I mention a willingness to lower my bid, however. Why wouldn't a client take the opportunity to ask for a lower price, regardless of whether it's merited? I'd just be opening myself up to unwanted and pointless haggling. Implicit in the nature of freelancing/contracting work is that almost everything may be negotiable, so the client is quite free to ask me for a lower price without my offering it.
Besides that, any enticing of clients on the basis of price is best done in the bid amount box. If the client rejects your proposal on the basis of price, your suggesting a lower price in the text of the proposal may never be read.
