I would prefer if you had given the reference. Not everything you read is true; this itself is a truth that many people have trouble learning. I think I was sent this question because I am already on record on this topic. I personally would just have referred you to my previous answer... but here goes.

One thing I would change from my previous answer: there are enough really, really big bones around that we can no longer say with confidence that "no dinosaur was as big as the modern blue whale." But they were still land animals, and fully capable of holding their own against gravity!

1. There is no reason to think the Earth's gravity is any different today than it was in the past. None. Nada. Zilch.

2. Whales are not land animals. Normally water buoys up their mass, and they don't need to have gravity-resisting muscles. So when they are stranded on land, they suffocate because they don't have the muscles to breathe against gravity. This has nothing to do with size. Very small whales (dolphins and porpoises, which mass a lot less than land animals like elephants or hippopotomi or rhinoceri) can't live long out of water either, for the same reason as the giant whales.

3. Dinosaurs were land animals, with the skeletal (and muscular) framework to deal with the pull of gravity. They could breathe on land, they could move on land, they could and did thrive on land. This is not just conjecture along the lines of "they lived on land, they must have been able to breathe!" The muscle attachment scars on dinosaur bones give us a good idea of the muscular power of the beasts. And large dinosaurs were powerful indeed!

4. Sauropods (the Brontosaurus types) had the same sort of blood-to-brain problem as the modern giraffe, which gets blood to its brain quite well, thank you very much. Why do you think sauropods had such small heads? Their heads were as large as they could be, given the limitations of forcing blood up that long, long neck. Anyhow, how does your source know that no sauropod could have had a heart adequate to the task of pumping blood to its head?

   Last I saw (Walking with Dinosaurs, the companion volume to the BBC-TV series) it is thought that sauropods grew so large because they had to process coarse vegetation entirely in their guts -- no dinosaur until Iguanodon, quite a while later, was able to chew. Because food processing was entirely stomachic and intestinal, the sauropods needed long guts, and large bodies to hold them. Long necks may possibly be

   1. to reach higher vegetation than other herbivores or, more likely (?),
   2. to allow maximum grazing for minimum actual bodily movement.

5. Robert Bakker (not the least controversial of dinosaur paleontologists) believes that dinosaurs set and explored the size limits for land-living animals. See his book The Dinosaur Heresies.

I'm sorry if I got a bit snippy, but the piece of misinformation you were fed is not only a canard (French for "duck") but a mighty lame duck, too.