I'm with you on that. Just saying that the 25% chance factoid in isolation is a little bit misleading. One team has a 25% chance of getting the #1 pick, but the other teams are still dividing their picks up from the remaining 75%.
i.e. Portland's (#1 pick) 250 lottery balls out of 1000 is a lot nicer than Charlotte's (#3 pick) 138, to use an example from the 06 draft. That's something that often gets swept under the rug when that figure is pulled up.
A few other things that get swept under the rug quite often in these discussions are a) the chance to miss out on a top 3 pick is bigger than the chance to get one and b) the Celtics aren´t in the lottery every year.
The odds of which record gets to pick first are the average odds, they have no actual meaning for a single team within a particular lottery. Sure, you can say "on average, the odds for the worst record to pick first are 1 in 4", but as people like to say, it´s called a lottery for a reason. Unless you plan to be in every lottery (and who would want that?), it doesn´t make sense to play the odds.
If the Pistons had won 1 more game last season, they would´ve picked 3rd. If the Cavaliers had won 1 more game in 11-12, they would´ve gotten Anthony Davis instead of Dion Waiters. If the Timberwolves had won 16 more games in 10-11, they could´ve picked Irving instead of Derrick Williams.
The best thing about the worst record is the 100% chance of picking in the top 4, not the average odds to get a pick in the top 3.
This supposed trade-off between increased average odds against decreased value of 15 potential trade chips doesn´t actually exist, as one is some abstract, theoretical projection while the other are 15 very real Celtics players under contract.