It's not really that our peception may only have a limited access to the true nature of things - it's that all the concepts embodied in that statement are artifacts of the way we perceive and conceptualise things, and it's only these that we have access to. What we think is the world is actually a simplified simulation of it wholly contained in each of our minds. It is my belief that this is anchored to a genuine objective world outside my head through my low level senses, but I have no direct access to these low level senses. For example, the image on my retinas goes through masses of processing and interpretation before it gets anywhere near my conscious perception; what I see is actually coloured strongly by all the templates I have absorbed since childhood that help me to individuate objects and interpret what they are. If I did have conscious access to the individual flickering pixelations on my retinas, it would probably not make a lot of sense to me. This goes very deep, because we project without thinking highly structuring concepts such as 'thing' onto the world, but this is a human mind artifact par exellence - the separation of the world into distinct objects is an artifact of our minds rather than part of objective reality. I'm not talking about language and naming things here which is secondary - I'm talking about our mechanisms of perception before we express something in words.
Time is another problem too. We presume that there is a past and a future history, but all I'm actually aware of when I stop and think about it is here, now. I can't go back five minutes to convince myself it was really there, not can I go forward five minutes to check that it will be. I cannot verify directly that the past existed.
So all I can be certain of is what I am aware of inside my mind in the present moment - there's no way I can get outside myself to see if there really is a world out there separate to myself. I believe that others with far more philosophical ability than myself have tried and failed to overcome that barrier. What I can do though is to make a free choice and believe that there is an external reality. While accepting that there can be no certainty that I'm right, it's the choice that seems most consistent with the way my world presents itself to me (and it's much more comfortable to believe that too
). But like you say, the world that I perceive, granted that it really is there, is both like but also very unlike how I perceive it.
You might wonder where all this sort of thinking comes from, but when I was a child of about seven or eight, I woke up one morning and noticed that the world didn't look real - it was one of those moments that coloured my life since then in many ways. It's been a long story since then, coming to terms with it and finding that there is no hard edged resolution to it. It's strange that it has led me to the conclusion that I have to decide what reality is as much as to perceive and understand it.