It's no secret how MicroStrategy buys BTC without affecting the price - they do it through Coinbase, which again uses different methods to provide the customer with a satisfactory result.
Makes sense, US company using a US exchange to buy huge amounts of crypto. I don't see how else a publicly-traded corporation would do it. If they bought from an individual whale, there might be questions from shareholders (or short-sellers) about conflicts of interest and so forth; and it wouldn't be great for MSTR's public image if they used a foreign exchange, nor would it likely be advantageous for them to do so.
And OP, I wouldn't call what Michael Saylor has as "bags". For one thing, the bitcoin isn't his. For another, what MSTR owns is a huge amount of bitcoin, the king of kings when it comes to crypto. "Holding the bag" implies that you've bought something lousy, and that doesn't describe bitcoin at all.