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>We have no idea what decay rates were in the distant past.
>We just ASSUME they were the same as today.

For what it’s worth...

We can be confident that radioactive-decay rates have not varied over geological time for several reasons:

1) There is no known physical reason that would cause them to vary noticeably. The two main types of radioactive decay used for radiometric dating are alpha and beta decay, which are both well-understood physical phenomena, and which have rates that can be calculated from the decay energies and various fundamental physical constants. In particular, alpha decay takes place by quantum-mechanical tunneling; the emitted helium-4 nucleus spreads through its “forbidden” region near the nucleus to where it can escape. And beta decay takes place by the weak elementary interaction, which can convert neutrons and protons and emit or absorb electrons.

The electrons in decaying atoms do have an influence on their decay rates, but all but the outermost ones are essentially unaffected by different states of chemical combination and different pressures in the Earth. In particular, it is mostly the innermost electrons that are captured in electron-capture decay, and these are relatively unaffected by the outside world. The main exception, beryllium-7 (which is not used for radiometric dating, hence any anomalies in its decay are irrelevant to the question of whether or not radiometric dating techniques are valid), is easily accounted for by noting that its outermost and innermost electrons are right next to each other (beryllium has only 4 electrons in 2 shells with 2 each).

2) If such variations happened, then it would be very unlikely that they would happen in exact sync, which is what would be necessary to produce the observed concordances. In fact, if such discrepancies existed, it would be possible to produce plots of U-Pb age vs. K-Ar age. However, searching for such discrepancies has resulted in some sensitive upper limits, as described in The fundamental constants and their variation: observational status and theoretical motivations

3) The physics of stars (and other objects) which we can observe is independent of how far they are away from earth. Observing stars which are very far away means also looking very far back in time. The physics of stars is strongly dependend on nuclear reactions and thus also connected to decay rates. Therefore a change in decay rates which would affect the accuracy of radiometric dating can be clearly ruled out.

4) Studies on the isotopes left behind by the Oklo reactor, a natural occuring nuclear reactor about two billion years ago, are giving an upper limit of the change of constants and excludes changes in constants which are big enough to affect the accuracy of radiometric dating.

http://evolutionwiki.org/wiki/Radiometric_dating#Creationist_claims_about_radiometric_dating