This is both right and wrong.
First we have to see what "raise the price" means. Going from $1 to $2 is a $1 rise but percentage wise it is a 100% increase. However going from $1000 to $1001 is also a $1 rise but it is a 0.1% rise. The former will take a much bigger amount of money compared to the later. So we have to first take percentage rise into consideration which is what people usually forget. An stock example is Berkshire Hathaway that got dumped $5936 in the past 24 hours but that was 1.35%.

Secondly we have to take adoption into consideration. Bitcoin is not like other things, it is on the growth. This means as we move forward we see an increasing amount of people adopting bitcoin and they are bringing a lot more money in total, so it is understandable to see price rises take place even faster than before.

But how much money it takes to go up 1% for example, depends on how packed the orderbooks are not what the price is. For example if the order book from $1 to $2 is $10 million but from $1000 to $2000 is $9 million it still is easier to do the later.
This is what we sometimes see when we have a quick jump. Like from $3800 to $6200 in a couple of days. Or the recent 63% rise in 19 days from $41k to $67k.