That is the logical and correct (in my opinion) way of looking at it. I agree with you.
Buying at the bid supports a price, it doesn't depress it. Selling at bid is what puts downward pressure on a price. Selling at ask supports a price, while buying at the ask puts upward pressure on the price.
If the company cannot purchase shares at a given bid, then they are forced to move that bid up with the increasing price. If a large seller steps in then the company supports that price by buying those shares at bid. Pretty simple really. So we can assume the company is sincere about buying shares, which means it will support prices, which also means any other new buyers are battling at the same bid as the company. Hopefully those new buyers become impatient and hit the ask for shares, which will eventually drive the price up.
The question becomes at what price and date will the company start buying shares and create a bottom for us?