I think it's likely to be intentional price manipulation to make someone's portfolio look better (worth more in market value terms). I know that Commsec are always on the lookout for small trades that move share prices a lot, as I've had trades blocked by them and had to ring them up and explain that my trade was legitimate.
In one case, I was trying to sell out of a stock and all but 3 of my shares got bought so I moved the sell price down to the highest buy price just to get rid of those last three shares as part of the same trade (so as not to be left with 3 shares in a microcap with a share price of sub-20-cents). I was told that they couldn't accept the price change because it was too much of a change in percentage terms, so I had to do it in smaller increments, so after 6 trade modifications I finally offloaded those three shares.
In another case, a few years back, I was trying to complete a buy trade that had a small handful of shares outstanding (so, like, 99% of my trade had gone through but not the other 1%) and I like big round numbers when possible, so I would prefer to hold 10,000 shares in a company than 9,912 shares, especially if they pay dividends, so I was prepared to move the buy price up just for those last handful of shares (the bulk of the trade having already gone through at a lower price). They didn't like that either.
Neither of those cases are in any way similar to the small trades that you are both referring to with Stealth. I'm just saying that some online brokers (i.e. Commsec) are aware of price manipulation and are trying to stop it when they can (and also blocking some legitimate trades in the process), however other brokers are not particulary interested. I now do a fair amount of my trades through SelfWealth (for their $9.50/trade flat fee) and I can't recall them ever having queried a trade or a trade modification (price change).
If you had free or next-to-nothing unlimited brokerage available, I guess it might be tempting to spend a couple of bucks on a few shares to bump up the share price of one of your portfolio positions just prior to preparing a report or something, however it is only going to be temporary window-dressing. The price will always come back to where the buyers and sellers meet on price.