"All-cash" is a widely misunderstood and misused term as it relates to real estate transactions. When sellers are looking for an all-cash offer, they are looking for an offer that does not require financing from the seller, and that does not contain any contingency for financing from any other source. It means that if the buyer does not deliver all cash to the seller on or before the stipulated closing date, then the buyer agrees to forfeit their good-faith deposit to the seller.
I have yet to see a real estate contract that restricts a buyer's ability to obtain financing as part of their source of cash to the seller. In an all-cash transaction, however, the seller has no obligation to participate in the financing activities of the buyer, and has every right to keep the buyer's deposit should they fail to deliver the full amount in cash at closing, on or before the closing date.