[MI][Condo] HOA Management company sent out a highly inflated bill for water leak repairs seemingly not allowed by the Bylaws, won't respond to inquiries about it. Please help!

Backstory: Our water heater failed due to old age in the middle of the night and sprung a leak. We caught it within a few minutes, but not before some water leaked into the unit the ceiling of the unit below us and was leaking out a few of their light fixtures in their kitchen. The neighbor called the emergency number for the management company and they sent out their on call guy to assess the situation. We had already shut off the water, stopped the leak, and drained the tank, by the time guy arrived. He took a quick look around and left. The guy goes down to the neighbor's (still the middle of the night) and cuts a few holes in the drywall to help get the water out / help it dry and leaves. He comes back the next day with an industrial dehumidifier for each of our 2 units to run for a few days. A few days later he comes and gets the dehumidifiers. He did some repair work to their unit. We hired a company to replace our water heater and paid for that.

About 2 months later we get a bill from the HOA's management company for over $3k. It's full of inflated charges, in the style of hospital bill with a $50 aspirin. There are charges of $150 an hour charge for the labor of their on call employee for many hours. And over $900 for the use of the two dehumidifiers. The notes with the invoice makes it very clear the management company owns the dehumidifiers and had them in their own warehouse and they incurred no actual expense from us using them. Other things like $20+ for a trash bag and "disposal". They used less than one 4x8 sheet of drywall to repair the unit below ours that they drastically over-billed for.

We were told we had to accept the dehumidifier. We were not told there would be a charge for it. We never agreed to pay or reimburse anyone for anything related to this incident verbally or in writing.

I've read the governing bylaws for the association quite closely repeatedly and I can't find any basis for them to charge us for for their "costs" for this or really any costs related to the repair. The bylaws say the owner of the affected unit has to pay for things not covered by the HOA's insurance. The management company is hired and paid very well to manage the property. It seems like they are charging us for expenses related to managing the property.

We have sent the HOA management company polite and well written e-mails both to the person who first emailed us the invoice and their general contact email on different occasions asking for an explanation of the charges, stating that we did not hire them, that we did not agree to pay their expenses, and ask for clarification under what article & subsection of Bylaws they are claiming we are responsible for these charges. We have gotten no replies other than the, "Thanks for contacting us. We received your e-mail and will reply in 24-48 hours" auto-reply. They don't reply. They continue to pursue the charges against us sending us invoices in the mail demanding payment, threatening late fees, etc. In the mean time, we continue to pay the monthly association dues.

To me it feels like they are on a fishing expedition hoping that we will either pay their invoice or have our insurance pay it. It seems to me (not a laywer) that they have no legal standing to collect this money from us or they would have replied to our inquiries explaining how we legally owe them this money. That said, because of their business relationship with the HOA and thereby also us I'm not sure we can just ignore the invoice and hope they go away. I suspect we could get a lien on the property.

What should we do or our next steps be?

Thanks!