Sounds like someone is a Java hater, or perhaps just living in the past.
For quite some time now, Java's garbage collection times have been negligible. With every release of Java, things are being improved everywhere, including the front on garbage collection (in Java7, which releases later this year, comes the G1 Garbage Collector, the latest and greatest from Java). If you are experiencing issues with garbage collection, perhaps the issue is actually a memory leak in either your code, or the third party jars that you are using.
While I AM a dedicated follower (and believer) of Java, I think it is fair to note that Android simply uses Java syntax. Android code is not compiled to java byte code, but rather into .dex files which are read by a Dalvik Virtaul Machine. I do not know how DVM handles garbage collection currently, but I am sure it is doing a fine job.
All in all, I am suggesting that you don't worry about 'the dreaded garbage collector', but instead worry about writing solid code