Not in the case of one photon, but in the case where you repeat the experiment.
No matter how many times you run the experiment, 2 detectors will always show an interference pattern. 2 detectors will always show a clump pattern. This is despite the fact that there is no empirical difference between the detectors from the photons point of view. If it was random (the emitted photons start life by going through slits randomly) then we would see a random distribution of clumps and interference patterns at each detector. But we don't. So it seems that our knowledge of the system (that some detectors give us which path info and some don't) predetermines the photons to act in a particular way.
What you're talking about is sometimes called the instrument effect (although the observer effect is it's true name). If you want to detect something, you have to fire a photon/electron/something at it (so it can reflect back to give you information) which affects what you're looking at.
The real weird thing about the delayed choice experiment comes later in the video, with the
entanglement delayed-choice swapping. The usual confusion about the collapse of the uncertainty in QM comes from the fact that what 'collapses' when you look at it is the wavefunction, not the physical object. (The wavefunction is just a representation of the particle which contains all the possible information about the particle so it's not surprising that once the particles actual properties are known it shrinks down from a range of possibilities to just one). However the delayed entanglement swapping
seems to bypass that, which really blows my mind. Realistically I'm going to put it down to quantum weirdness. The universe is a strange place (I posted about
simultaneity earlier, which is equally fascinating but concerns relativity rather than QM). I revisit these experiments about once a year (I don't study physics any more so unfortunately my understanding seems to worsen over time rather than increase) but each time it never ceases to amaze me.