I doubt that the empirical data actually supports this assertion.
In other words, I doubt that merely increasing the fee solves the spam problem and causes your transaction to go through in a timely or expected manner.
Yes, increasing the fee does surely almost guarantee it.
It doesn't solve the spam problem though... as spam will keep increasing the number of unconfirmed transactions in the mempool... but that's something that won't affect your
properly generously paid transaction.
For illustration, this is like a BUS system transportation, in which, when the BUS is empty, people can board for free or for a small fee, but paid travellers can always buy their seat.
When there is enough paying people to fill the BUS, all the rest can keep in the queue but there's no place for them, so they have to wait. If there is more people willing to pay that capacity in the BUS, you can always pay more than the rest to make sure you get your seat. As long as you are willing to pay enough, your seat is garanted, no matter how many are crowding outside waiting for their free/cheap ride.
Now take into account that many of people waiting outside in the queue doesn't really want to get onto the bus, they are just in the crowd complaining about how expensive the BUS now is, that they can't get on it for free anymore, and that they have been waiting for days to get a cheap seat.... while the paying passengers are just flowing as always (paying a higher fee as before though).
Sure if the price is not moving too much, you can make these kinds of assertions, but in the end, we don't really know for sure if there were coins that were delayed in being moved and therefore delayed in being dumped in order to lower the price.
Even if they were delayed... they were delayed since when?
Even if you consider a 2 days delay (what?!) that does mean that after two days all the coins arrive at the exchanges and its only the next ones that are yet to be received. So theres not much impact from that, just some lag (again the two days figure is an extreme exageration).
Unless you are considering that this fee/delay problem is something new that just hapenned since the last hours/days.