I recently brought my car in for a 175k recommended maintenance (oil change) and when about to drive out of the dealer i heard a loud knocking sound from the engine. I asked them to keep the car and take a look at what that could be. The dealer called me back a few days later with a list of problems including a "slipping time chain tensioner" and a bad "cam shaft gear". The sounds I was hearing was nothing I ever heard before on a car with no previous engine problems. In addition they told me that when taking out the cam shaft gear they will need to replace the radiator. Does it make sense that while doing the oil change the dealer did something by accident (or on purpose) that would cause these issues? Thanks in advance.
This is likely to be coincidence - changing the oil and filter is not work likely to cause the timing chain or tensioner to fail.
Timing chains can slip / fail once sufficiently worn.
You don't mention the make / model or engine type, but some engines are well-known for being more likely to suffer this type of failure once they are "older".
It would be helpful to know what type of car you have as some of the timing chain tensioners (I know some 2008-12 VW do) rely on oil pressure to work correctly. If the engine was run without first priming the oil filter then I can see that this would cause issues with an oil dependent tensioner.
It would also help to know if the place used for servicing is a specialist or manufacturer approved workshop for the make of car in question. If so, it is less likely (although not impossible) that they'd have forgotten an engine specific process.
Also, if the cam buckets are of the hydraulic type, it's concivable that this could have a negative effect on the cam shaft gear if sufficient oil pressure were not present at initial engine start.
Finally, feel free to have another mechanic to assess the vehicle. It's always worth getting a totally independent third party professionals opinion. Especially if it's likely that they may be negligent.