I would not be concerned with disclosing the communities financial documents to the management company. The financial and governing documents are public documents available to the whole community, and any management company considering taking on the responsibilities of managing the HOA would likely need this information to understand the community's needs and obligations fully.
The price the management company sets is typically based on a multitude of factors, such as number of units, age of the community, common areas, community amenities, and other factors that could influence their management approach. The financial health and stability of the HOA may also play a role in determining the price as well. However, this doesn't necessarily mean they set their price solely on how much money the HOA has.
I would start by asking the company about their pricing structure and how they use the information to determine their fees. Transparency and open communication are key to a successful partnership with a management company.