More or less true. The footage from the British film 'The Battle of the Somme' of soldiers going over the top for example is a recreation of the first day of the attack. There's considerable amounts of footage of soldiers marching and artillery firing, which is all real, for a given value of real, but while I've heard of there being actual combat footage, I don't think I've seen any that was actually used.

Firstly videography was a new technology and still moving image cameras were still expensive, bulky and fragile. The Aeroscope camera seen here was one of the first able to be used for military videography. It was procured in large numbers by the British War Office for military cameramen and much of the British WW1 footage we have is filmed on them. But there were still numerous drawbacks to trying to get footage of forces in action. The cameras were still relatively large and unwieldy, they were expensive, they could only hold enough film for 10 minutes of footage and were easily damaged. While the Aeroscope used compressed air to turn the reel, most other cameras were hand cranked, meaning they had to be set up on tripods and were even bulkier, if somewhat more robust. Attempting to film close up shots or wide shots was difficult with the cameras available and according to the Imperial War Museum British cinematographers "found it impossible to capture close-ups of men climbing out of their trenches. They consequently filmed staged recreations of 'over the top' scenes for inclusion in the final film." The IWM has a short article about the making of the Battle of the Somme film, which covers some of these points and the blog Shooting the Great War covers many aspects of WW1 cinematography as well as I've seen anywhere.

The second part of your question is really about censorship and propaganda. It was about how the populations of warring nations were allowed to see the war and what they were encouraged to think about it. All British empire soldiers were banned from taking cameras into the trenches, partly for military reasons, if the camera is captured its contents may give the enemy valuable information, and partly because there was no telling what soldiers would take pictures of and how that material would be distributed. Official correspondents were discouraged from capturing graphic images of the dead and wounded, and if they did take them they were unlikely to be published. The governments wanted images and film produced to give an impression of the strength, human, mechanical and industrial, of the nation at war. They wanted to show happy, contented soldiers to assuage the worries of families at home and just enough action to excite people for the war effort. Showing exact conditions of the front lines or images of the dead and horribly wounded would have the opposite effect and was either discouraged or outright banned.

But as the war went on the photographers in particular started ignoring these dictums and more graphic images of the dead such as this one and this one were taken, whether they were published at the time or not.