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no you are correct those pads should slide by hand into the pad clips by hand
if the clips are new or no rust on top or under them then file down or grind a little on each side of the pad ( should not take much filing or grinding ) and then make sure to lube those pad to clip contact points with brake grease
and when your done they will be all lubed up and the pads should slide in by hand !
The clips are brand new. Even the factory pads were very tight. How easy should they slide in, or how easy should the pads move back and forth in the clips once installed?
you should be able to push them in with one hand and slide back and forth in the clips with 1 hand
a lot of times even the factory fads will do this with extra on the ends causing this a simple sand down or quick grind will do the trick and don't forget the brake grease