The key here is to determine what you mean by ‘real’ value of debt.
The market value reflects the cash a party would pay to buy all the debt on the market (excluding transaction costs and ignoring liquidity/friction costs). That’s relevant in M+A for instance to MtM a balance sheet. Or in some distressed situations, when debt holders agree to haircut par amounts at a level consistent with market levels. Happens but not every day.
If one wants the amount of debt outstanding, to assess leverage, then you’d take the par amounts drawn and translated at spot FX. Book value is a reasonable proxy, but is not the same as book value includes transaction costs and hedging, amortised at the effective rate. For issuers that regularly come to market, the difference can be significant, ive seen up to a third of a turn of EBITDA.
As a result, none of the commercial databases including bloomberg give the correct amount of debt. But the market doesn’t care, because for those instances where the difference matters, like in distressed debt work, people dont price the securities based on data from commercial databases anyways.